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Computational Accounts of Attentional Bias: Neural Network and Bayesian Network Models of the Dot Probe Paradigm

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PAGE 1

COMPUTATIONAL ACCOUNTS OF ATTE NTIONAL BIAS: NEURAL NETWORK AND BAYESIAN NETWORK MODELS OF THE DOT PROBE PARADIGM By AMITOJ SINGH LIKHARI A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN EXERCISE AND SPORT SCIENCES UNIVERSITY OF FLORIDA 2005

PAGE 2

Copyright 2005 by Amitoj Singh Likhari

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This thesis is dedicated to my family, esp ecially my Dad, Sarab Jit Singh, who always pushed me to follow my heart and gave me th e reason to pursue this Master’s. My Mom, Sukhjinder who patiently supported me thr ough every step of the way. My sisters, Tanvir and Kamalpreet, and my brothers-in-law, Parneet a nd Dhananjay, for helping and guiding me find what I truly believe in. Last but not least, my three nephews, Sukhsahegj, Sarguun and Manu, for making me realize that things were not that bad after all.

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iv ACKNOWLEDGMENTS Countless hours have gone into the preparation of this th esis. However, I could not have made it if I did not have people pushi ng and prodding me to do better. I would like to thank Dr. Christopher Janelle, my adviso r, for helping and supporting the idea of my thesis even when it was not as concrete, and for letting me down easy on the numerous occasions that I presented him with what su rely must be the worst writing possible. I would also like to thank my friends and peer s at the Motor Behavior Laboratory at the University of Florida, Steve Coombes, wit hout whose data and revisions to text, this work not have been possible, and Sarah Huie for proofreading my fi rst drafts and going a long way in improving the quality of this work. Special thanks go to Dr. Anand Rangarajan, Associate Professor at Computer and Information Science and Engineering, at the University of Florida, for helping me solidify the concepts and asking me questions to force me to think clearly. Over the last few weeks, I have spent a significant amount of time at the library, and I thank the one person who agreed to study there with me, Angela Duke. Finally, none of this would not have been possible if Aaron Duley, also of the Motor Behavior Laboratory., had not first sugge sted the idea of developing a computer simulation.

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v TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................iv LIST OF TABLES.............................................................................................................ix LIST OF FIGURES...........................................................................................................xi ABSTRACT......................................................................................................................x ii CHAPTER 1 INTRODUCTION........................................................................................................1 1.1 Cognitive Models of Anxiety.................................................................................2 1.2 Computer Tools to Investigate Mechanisms of Attentional Bias...........................4 1.2.1 Neural Networks...........................................................................................4 1.2.2 Bayesian Networks.......................................................................................5 1.3 Previous Research...................................................................................................5 1.4 Limitations..............................................................................................................9 1.5 Statement of Problem...........................................................................................10 1.6 Statement of Purpose............................................................................................10 1.7 Current Study........................................................................................................10 1.7.1 Objectives of the Neural Network Model..................................................11 1.7.2 Objectives of the Bayesian Network Model...............................................12 1.8 Hypotheses............................................................................................................12 2 REVIEW OF LITERATURE.....................................................................................14 2.1 Anxiety.................................................................................................................15 2.2 Attentional Bias....................................................................................................22 2.2.1 Dichotic Listening Paradigm......................................................................23 2.2.2 Stroop Task.................................................................................................24 2.2.3 Dot Probe Task...........................................................................................29 2.2.3.1 Initial studies (basic dot probe task).................................................30 2.2.3.2 Manipulation of stimulus duration...................................................37 2.2.3.3 Backward masking...........................................................................38 2.2.3.4 Pictorial dot probe task.....................................................................39 2.2.3.5 Social anxiety...................................................................................42

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vi 2.2.3.6 Drug abuse........................................................................................44 2.2.3.7 Smoking and alcoholism..................................................................44 2.2.3.8 Eating disorders................................................................................45 2.2.3.9 Pain and miscellaneous areas...........................................................46 2.2.3.10 Limitations of the dot probe...........................................................46 2.3 Connectionist Models of Attention.......................................................................46 2.3.1 Neural Networks.........................................................................................48 2.3.1.1 Overview..........................................................................................48 2.3.1.2 Learning...........................................................................................49 2.3.1.3 Supervised learning..........................................................................50 2.3.1.4 An example of supervised learning..................................................50 2.3.2 Details and Theory.....................................................................................51 2.3.2.1 Overview..........................................................................................51 2.3.2.2 Notation............................................................................................53 2.3.2.3 Initialization.....................................................................................54 2.3.2.4 Node Details.....................................................................................54 2.3.2.5 Net input...........................................................................................54 2.3.2.6 Activation level................................................................................55 2.3.2.7 Output...............................................................................................56 2.3.2.8 Training............................................................................................57 2.3.2.9 Testing..............................................................................................59 2.4 Connectionist Models of the Stroop Task............................................................59 2.4.1 The Cohen Model.......................................................................................59 2.4.1.1 Structure...........................................................................................60 2.4.1.2 Initialization.....................................................................................60 2.4.1.3 Net input...........................................................................................61 2.4.1.4 Activation.........................................................................................62 2.4.1.5 Output...............................................................................................62 2.4.1.6 Training............................................................................................63 2.4.1.7 Testing..............................................................................................64 2.4.1.8 Simulations and results.....................................................................65 2.4.2 The Matthews and Harley Model...............................................................66 2.4.2.1 Hypotheses.......................................................................................67 2.4.2.2 Structure...........................................................................................68 2.4.2.3 Initialization.....................................................................................69 2.4.2.4 Input.................................................................................................69 2.4.2.5 Output...............................................................................................69 2.4.2.6 Training and testing..........................................................................69 2.4.2.7 Results..............................................................................................72 2.4.3 Pros and cons of using PDP models...........................................................73 2.4.3.1 Advantages.......................................................................................73 2.4.3.2 Criticisms.........................................................................................73 2.5 A Belief Network Model of Attenti onal Bias in Dot Probe Paradigm.................74 2.5.1 Nothing is Certain...............................................................................75 2.5.2 Axioms of Probability.........................................................................77 2.5.3 Law of Total Probability.....................................................................78

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vii 2.5.4 Conditional Probability.......................................................................80 2.5.5 Chain Rule...........................................................................................80 2.5.6 Bayes’ Theorem..................................................................................81 2.5.7 Conditional Independence...................................................................82 2.5.8 Graphical Notation..............................................................................83 2.5.9 Causal Networks and d-separation......................................................84 2.5.10 Bayesian Networks............................................................................85 2.5.11 An Example of a Bayesian Network.................................................90 2.6 Summary...............................................................................................................94 3 METHODS.................................................................................................................95 3.1 The Task...............................................................................................................96 3.2 Neural Network Model of the Dot Probe task......................................................96 3.2.1 Mechanisms................................................................................................97 3.2.1.1 Baseline condition............................................................................99 3.2.1.2 Exposure mechanism........................................................................99 3.2.1.3 Interaction mechanism...................................................................100 3.2.1.4 Intensity condition..........................................................................101 3.2.2 Simulations...............................................................................................102 3.2.3 Structure...................................................................................................102 3.2.4 Net Input...................................................................................................103 3.2.5 Activation.................................................................................................103 3.2.6 Output.......................................................................................................104 3.2.7 Initialization..............................................................................................105 3.2.8 Training....................................................................................................105 3.2.9 Testing......................................................................................................105 3.3 Bayesian Network...............................................................................................105 4 RESULTS.................................................................................................................110 4.1 Neural Network Model.......................................................................................110 4.1.1 Results for Simulation 1: RT....................................................................113 4.1.2 Results for Simulation 2: Activation........................................................117 4.2 Bayesian Network Model...................................................................................119 5 DISCUSSION...........................................................................................................124 5.1 Neural Network Model.......................................................................................124 5.1.1 Weights of the Network............................................................................125 5.1.2 Performance of the Training Mechanisms...............................................126 5.2 Bayesian Network...............................................................................................129 5.2.1 The Conditional Probability Tables..........................................................129 5.2.2 Interpretation of Probability Values.........................................................132

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viii 5.2.3 Testing Against Actual Data....................................................................132 5.3 Statement of Limitations.....................................................................................133 5.4 Future Research..................................................................................................135 5.5 Summary and Conclusion...................................................................................136 APPENDIX WEIGHTS AND BIASES OF THE NEURAL NETWORK MODEL...........................137 LIST OF REFERENCES.................................................................................................139 BIOGRAPHICAL SKETCH...........................................................................................148

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ix LIST OF TABLES Table page 2.1 Input patterns and corres ponding outputs used for traini ng the network by Cohen et al. (1990)..................................................................................................................64 2.2 Training patterns and number of times each condition was presented to the network to train for the emotional Stroop task...........................................................................71 3.1 Training patterns used to train the NN for baseline, exposure 3x and exposure 5x conditions.................................................................................................................98 3.2 Training patterns for the at tention mechanism for baselin e, exposure 3x and exposure 5x conditions............................................................................................................98 3.3 Training patterns used to train the network for the inte raction mechanism..............101 4.1 Number of training iterations a nd MSE for each training mechanism......................110 4.2 Basic test patterns for the neural network model.......................................................112 4.3 Test patterns for the intensity condition.....................................................................112 4.4 Results of Simulation 1 under conditions of high anxiety.........................................114 4.5 Results of Simulation 1 under condition of low anxiety............................................115 4.6 Simulation 2: Output activatio ns for high and low anxiety.......................................118 4.7 Conditional probability tables for variables Arousal Rating (AR ), Anxiety ( Anx ), Probe Side ( PS ), and Reaction Time ( RT )..............................................................120 4.8 Conditional probability tables for vari able AR for the Bayesian network................120 4.9 Posterior probabilities of various variables computed given the evid ence (in bold) using the CPT derived from all data.......................................................................121 4.10 Posterior probabilities of various variab les computed given the evidence (in bold) using the CPT derived from data using pictures appearing on the left only..........121 4.11 Posterior probabilities of various variab les computed given the evidence (in bold) using the CPT derived from data using pictures appearing on the left only..........122

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x 4.12 Prior and posterior probabilities for various prior probab ility values of AR= Neg. 122 4.13 Prior and posterior probabilities for various prior probab ility values of Anx= high 122 4.14 Prior and posterior probabilities of Anx= high for various prior pr obability values of AR= Neg given AD= neg. ......................................................................................123 4.15 Prior and posterior probabilities of AR= Neg for various prior pr obability values of Anx=high given AD= neg. .....................................................................................123 5.1 Conditional Probability Tables for vari able AR for the Bayesian network...............130 5.2 Posterior probabilities of various variables computed given the evid ence (in bold) using the CPT derived from all data.......................................................................132 A-1 Weights between the input and hidden units after training for baseline mechanism137 A-2 Weights between the input and hidde n units after training for exposure 3x mechanism..............................................................................................................137 A-3 Weights between the input and hidde n units after training for exposure 5x mechanism..............................................................................................................137 A-4 Weights between the input and hidden units after training for interaction mechanism137 A-5 Weights layer 2 (between the hidden and the output units) after training for baseline mechanism..............................................................................................................138 A-6 Weights layer 2 (between the hidden and the output units) after training for exposure 3x mechanism.........................................................................................................138 A-7 Weights layer 2 (between the hidden and the output units) after training for exposure 5x mechanism.........................................................................................................138 A-8 Weights layer 2 (between the hidden and the output units) after training for interaction mechanism............................................................................................138 A-9 Biases for hidden units for all training mechanisms.................................................138 A-10 Biases for the output units for all training mechanisms.........................................138

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xi LIST OF FIGURES Figure page 2.1 Cognitive mechanisms underlying biases in in itial orienting to threat in anxiety.......19 2.2 Versions of the Stroop task..........................................................................................25 2.4 A general multi-layer backpropagation neural network..............................................53 2.5 Details of a simple processi ng unit of a neural network..............................................55 2.6 Graph of the logistic sigmoid function........................................................................56 2.7 Flow of activation (solid lines) a nd error (dotted lines) in a multi-layer backpropagation neural network..............................................................................58 2.8. Neural network model for si mulation of the Stroop task............................................61 2.9 Matthews and Harley Model (a ) the first two models. The dotted lines were connected in Model 2 while non-existent in model 1, (b) model 3 shared the same connections for the 2nd weight layer with model 1. Connectio ns that differ in layer 1 are shown as solid lines while those carrying over from 1 and 2 are shown in dotted lines.....70 2.10 d-separation in (a)seria l, (b) diverging and (c) converging connections...................87 2.11. Illustration of conditional independence relationships.............................................89 2.12 A Sample Bayesian network to determine model the probability of the grass being wet given states of cloudiness ( C ), Rain ( R ) and Sprinkler ( S )................................92 3.1 Neural network model for simulating dot probe task................................................104 3.2 Bayesian network model of the dot probe task..........................................................108

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xii Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science in Exercise and Sport Sciences COMPUTATIONAL ACCOUNTS OF ATTE NTIONAL BIAS: NEURAL NETWORK AND BAYESIAN NETWORK MODELS OF THE DOT PROBE PARADIGM By Amitoj Singh Likhari May 2005 Chair: Christopher Janelle Major Department: Exercise and Sport Science Anxiety disorders afflict roughly 19 milli on American adults and their treatment costs upwards of 40 billion dollars annually. Attentional bias is believed to play a critical role in the etiology and maintenance of such di sorders. The dot probe paradigm is used to measure attentional bias. In order to develop be tter treatment protocols, it is essential to understand the mechanisms of attentional bias. The current study attempted to simulate human performance on the dot probe task using a neural network (NN) and compare thre e potential mechanisms of attentional bias. The NN accurately simulated performance for on e of the mechanisms called the exposure mechanism. The mechanism successfully produce d an attentional bias in the network by repeatedly applying negative inputs to it under conditions of high anxiety. The other two mechanisms tested were based on the inte raction hypothesis and intensity mechanism. The latter explains occurren ce of attentional bias through a increased in the perceived

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xiii threat value of salient stimu li by high anxiety individuals. The model also indicated a need to create a mechanism to simulate deliberate attention. The second part of the study consisted of building a probabilistic model of attentional bias in the dot probe task using a Bayesian network (BN) to uncover probabilistic relationships among the variables. The network wa s able to partially model the relationships among the variables. However, it proved to be unfit in its current form for the task; finer divisions are required to m odel data more accurately in the BN. On the whole, the model met with lim ited success but offered important insights and lessons that can be applied to building better models in the future.

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1 CHAPTER 1 INTRODUCTION Anxiety is typically considered a negative emotion that adversely affects the ability to attend to salient information required to complete tasks at hand (Woodman & Hardy, 2001). Distraction due to anxiet y can affect the information processing system to an extent that the affected i ndividual cannot perform tasks efficiently. Such a condition characterizes a wide spectrum of anxiety di sorders. Anxiety disorders are currently the most common mental illness in the United States today. Accord ing to the latest information available on the website of the Anxiety Disorder Association of America (ADAA, 2004), over 19 million adult Americans currently suffer from some form of anxiety disorder. Over 80% of these adults are afflicted by two specific disorders, namely, Generalized Anxiety Disorder ( GAD) and phobias. These two disorders are twice as likely to occur in women than men. On the whole, treatment costs for anxiety and related disorders approximate to $42 bill ion dollars a year. Clearly, a strong need exists to understand the nature and mechanis ms of these disorders to devise better treatment protocols. Anxiety affects an individual’ s ability to attend to task relevant cues in requisite detail by diminishing attentiona l resources available. Levels of trait anxiety reflect the propensity of a person to experience anxiety in a wide range of contexts, whereas state anxiety refers to the susceptibility to expe rience higher levels of anxiety in a given situation. Typically, individuals high in trait anxiety experi ence higher levels of state anxiety.

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2 Anxiety influences the dire ction of attentional alloca tion and how one processes information. Specifically, anxiety influences attentional bias which is defined as a discrete shift in atten tion to some change in the environm ent that is brought about either voluntarily or involuntarily (though typically the former) (W illiams, Watts, MacLeod & Matthews, 1997). According to some cognitive m odels, an attentional bias towards threat related information plays an important role in etiology and maintenance of anxiety disorders. 1.1 Cognitive Models of Anxiety Two such cognitive models are Beck’s sc hema theory (Beck, 1976; Beck, Emery & Greenberg, 1986; Beck et al. 1979) and associative networ k model of Bower (Bower, 1981). Both were among the most popular mode ls until the middle of the 1980’s. Beck’s schema theory proposed that all information was processed according to a set schema. In anxiety disorder the schema related to the proces sing of negative information became dysfunctional, thereby leading to selective processing of only negative information. This formed a cycle, with attention to ( negative ) threat related inform ation strengthening the schema, thereby rendering the individual unabl e to avoid attending to such information. Bower (1981) explained the same using an associative network. He posited that information was stored in an associative ne twork, with memories of events linked to emotions they evoke and vice versa. Accordi ng to Bower, anxiety caused an attentional bias towards threat. That is, nodes linked to threat information were activated more strongly and more frequently than others, leading to strengthening of the connections between nodes representing that class of info rmation. The increase in connection strength resulted in even small activation of a node ha ving a large overall effe ct. In other words,

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3 cues having a higher level of perceived thre at demanded a larger share of attentional resources. Both models suggested atten tional bias as the primary driving force responsible for causing and maintaining anxiety disorders. Bo th models however, incorrectly predicted an attentional bias toward information concerning loss or failure among depressed individuals. Williams, Watts, MacLeod and Ma tthews (1987) attempted to rectify this erroneous model by suggesting that anxiety is linked to an attentional bias towards threat information while depression is similarly biased towards recall of information related to loss or failure and as such is unaffected by the leve l of anxiety of the individual. They claimed that attentional bias was a product of the level of trait anxiety and the perceived threat value of the information. High trait anxiet y individuals orient toward the threat stimulus while low trait anxiety i ndividuals attend away from it. The main emphasis of research to date has been to understand causes and mechanisms of attentional bias. Causes include such attributes as the situation in which bias occurs, the threat value of the stimulus, trait and state anxiety levels of the person. Investigations into the causes are typi cally carried out by ex perimentation, using paradigms such as the dichotic listening para digm, the Stroop task, the dot probe and the visual search paradigm to observe and understand the nature of attent ional bias in various situations. Mechanisms on the other hand, refer to how the bias occurs and the location in the information processing system on which it acts (Williams et al., 1997). Typically, mechanisms are determined by formulating theo ries and models of attentional bias and verifying their correctness.

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4 1.2 Computer Tools to Investigate Mechanisms of Attentional Bias 1.2.1 Neural Networks A promising method that has been used to better understand the mechanisms is by modeling tasks that measure at tention. A popular tool for cons tructing such models is a neural network. A neural network (NN) (o r Parallel Distributed Processing (PDP) network) is a modeling method conceptually based on the functioning of the brain. NN models attempt to computationally mimic the massive parallelis m inherent in the structure of the brain. A NN m odel essentially consists of a number of processing units connected with each other with either excitatory or inhibito ry connections, thereby either increasing or decreasing activation levels of other processing units with which they articulate. The processing units themselves are constant, in that each unit performs the same computation. The critical element influe ncing the output of the network is the input to each unit. The input to a unit depends upon the weights on the connections between the unit in question and other units. As such, cha nges made to weights in the network affect the input to each unit, and ultimately the output of the network. Learning in the context of NN consists of determining the correct weight for each of the connections to accurately model the observed data from the problem domain. Learning in NN is essentia lly dichotomized into supervised and unsupervised learning. The model used in the present study follows supervised learning. Specifically, the network has to be “trained” with known da ta. Training in this context consists of supplying input with known output to the network. Weights on the connections between units are then adjusted until the network yiel ds the correct output for the given input pattern. This cycle is repeat ed on a large number of input patterns, until the network

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5 produces the correct output to all training patter ns. Details of this pr ocess are provided in the Chapter 2. One main advantage of using NNs to mode l cognitive phenomena is that they offer a precise computational account of the observed phenomenon consistent with the parallelism in the brain. Another advantag e is in the ability of NN to handle unknown data and situations using data from known situations and da ta, thus allowing statistical regularities to emerge without requiring explicit coding (Matthews & Harley, 1996). 1.2.2 Bayesian Networks A second method of modeling that has been gaining popularity in artificial intelligence and other industrial and statistical modeling settings but has not been used in anxiety research, is constructi ng probabilistic models of the variables involved in a task. The present study marks the firs t attempt to develop a probabi listic model of attentional bias using Bayesian networks (BN). BN allow intuitive probabilistic modeling of problem domains in which the relationships between variables ar e clearly understood. Such models rely on the laws of probabil ity coupled with subjective probabilistic relationships to perform probabilistic inference, from a quantitative standpoint. Although the study of attentional bias ha s matured to the point where th ese relationships have been empirically delineated, no attempt has been made to quantify these relationships. 1.3 Previous Research The Stroop task (Stroop, 1935) has traditi onally been the most popular choice for studies investigating attentiona l bias. Words are presented in different colored inks, with the participant being required to perform one of two tasks, color naming (naming the color of the ink) or word reading (reading th e word out loud). Typically, color naming is slower than word reading in conflicting conditions (i.e., wh en the word represents the

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6 name of a color different than the ink (C ohen, Dunbar & McClelland, 1990)). A generally accepted explanation is that becau se word reading is a more automatic task than color naming, the content of the word interferes w ith processing informa tion regarding color, and so causes the delay (Dyer, 1973; Glas er & Glaser, 1982). This robust finding has become commonly known as Stroop interference The emotional version of the Stroop task involves presentation of an emotional word instead of neutral words or color na mes. Color naming is slower for emotional words than for neutral words in this version. Interference in the modified Stroop task is explained as occurring due to the amount of effo rt required to shutout the content of the word, leaving fewer processing resources to perform color naming (Mogg & Bradley, 1998a). Otherwise stated, emotional words argu ably carry greater in formation load than neutrally valenced words, there by yielding higher reaction times. One shortcoming of the Stroop is in interpre ting the results; it is not clear whether the response latency is due to interference by the word content or diversion of attention from the word. This shortcoming of the St roop precludes the ability to locate where attentional biases occur over the course of information processing. In the absence of a valid alternative, the Stroop re mained the mainstay of attentional bias researchers for over five decades. Recognizing the significan t limitations of the emo tional Stroop task, MacLeod, Matthews, and Tata (1986) developed an attrac tive alternative to the Stroop that removed many of its shortcomings: The dot probe tas k. The dot probe task evaluates attentional draining rather than interferen ce to measure attentional bias. The basic task consists of displaying a pair of emotional stimuli (wor ds or images) simultaneously for a fixed

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7 duration. A dot (probe) appears at the spatial location of one of the stimuli following stimulus-offset. Participants are instructed to respond as quickly as possible to probe onset by pressing a button. The task was de veloped based on the hypothesis that high anxiety individuals oriented to ward threat stimuli while lo w anxiety individuals divert attention from the same. This hypothesis was supported by shorter re sponse latencies to dot probes appearing in place of the threat st imuli for the high anxiety group, and neutral stimuli in the low anxiety group. The dot probe has been used to uncover bi as in various disorders, including eating disorders, drug addiction, smoking, and trauma to name just a few by presenting cues related to the respective disorders to patients suffering from those. The task was the first to explain attentional bias without the confounding effects of interference, and has been very influential in the formulation of the model of attention by Williams et al. (1987) mentioned above. Further, the task presented a much clearer pictur e of the relationship between trait anxiety and attentional bias, t hough lacking clear explan ations of different roles of state and trait anxiety. The NN model of the classic Stroop task by Cohen et al. (1990) marked the first model of an attentional task using NN. With this simulation, they were able to replicate the major findings of the Stroop task better th an any other existing model. Up until that time, interpreting Stroop results was marred by its inherent shortcomings As a result all explanations of the results were open to di scussion and debate. The model explained the results on the basis of the training utilized to get the network to produce the desired results, using a concept called strength of processing (SOP). SOP refers to higher activation levels for the units for particular inputs, whic h occurred due either of two

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8 reasons; (1) an increase in stre ngth of connections between the processing units, and (2), higher resting activation levels of some input units. In other words, observed interference was explained building on the mechanisms used to produce the same interference in the network. Essentially, the model put forward thr ee different possible mechanisms of attentional bias which the authors refer to as (1) exposure (involving repeated exposure to the stimuli), (2) intensity (involving superactivating cer tain input nodes) and (3) attentional (involving implementing a specialized unit that simulated monitoring for threat and therefore influenced the activati on levels of the other units) mechanisms. The structure of the network consisted of two dis tinct pathways for the two tasks (explained in greater detail in Chapter 2) As such, it eliminated the possibility of ascribing Stroop effects to response interference, thereby providing a direct insight into the mechanisms without the confounds that mar interp reting results of the Stroop task. Matthews and Harley (1994) attempted to replicate the success of the Cohen model by building a model of the emotional Stroop task. There were two main differences between their model and that of the classi c Stroop (Cohen et al., 1990); firstly, the Cohen model simulated the time course of the psyc hological process (Cohe n et al. derived a relationship between the number of repetitions required to co mpute the output and the RT typical for the condition being simulated, a nd then presented results in terms of the computed RT) while the Matthews and Harley model did not. The second difference was that Matthews and his Harley sought to inves tigate specific mechanisms that had emerged from the first simulation rather than build the simulation to let the relationships emerge. However, the authors later acknowledged that ch oosing not to simulate the time course in

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9 the model limited its effectiven ess. Still, the model was ab le to successfully simulate Stroop interference for each mechanism. Despite its vast applications and popularity in studies of attentive disorders, no such model of the dot probe was developed until the current study. Although the dot probe has been used extensively to study attentiona l bias, it remains a method primarily to investigate the causes of bias and not th e mechanisms that underlie these biases. Although the collective empiri cal results are relatively coherent and consistent, conflicting results have emerged. For example, some studies of social anxiety have uncovered a bias towards socia lly threatening stimuli while others have not, leaving confusion about the mechanisms of this particular bias. Our hope is that modeling the dot probe task will yield potential answers to the questions while generating definite considerations for future research in this area. 1.4 Limitations Studies with the dot probe have yielded a vast database on various aspects of attentional biases. However, conclusions re garding the underlying mechanisms that drive these biases have been inferred from the data rather than directly investigated using models. As a result, although research with the dot probe paradigm has yielded robust relationships between the variables that comp rise the task, these relationships have not been clearly quantified for any of the samp les tested. Consider the relatively wellestablished relationship between trait anxiety, and valence and arousal level of the stimuli used in the dot probe task. Sp ecifically, individuals with high levels of trait anxiety react faster to probes replacing the negatively valenc ed stimuli. However, the specific values of trait anxiety, picture valence and arousa l rating are unknown. These and other variables of the dot probe task (e.g., stimulus duration, probe type, etc) cannot be easily quantified

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10 by variations in task methodology, but potential answers can be generated by manipulating the variables of the task in a computer simulation. 1.5 Statement of Problem Prior to the current study, research to study the mechanisms of attentional bias largely stemmed from studies of causes of attentional biases using paradigms such as the dot probe task. Little work had been done to directly investig ate the mechanisms by developing models that mimicked human beha vior when performing the dot probe task. Although studies using different modifications of the dot probe and similar paradigms yielded a huge amount of data, and significan tly advanced understanding of attentional bias, a model was needed that could be updated and verified (or challenged ) on the basis of new data. Further, although empirical work in this area is substantial, only a limited amount of data is collected from these studies thereby constraining th e analyses that can be performed. 1.6 Statement of Purpose The purpose of this study was twofold; firs t, I constructed a NN model to simulate performance on the dot probe task so as to investigate the underlying mechanisms of the task. Second, a probabilistic model of the paradigm was constructed using Bayesian networks to develop probabilis tic relationships between the variables of the model. The Bayesian model could also be viewed as a cau sal model and used to investigate the causal impact of one variable on the others. 1.7 Current Study No models had been developed to simu late human performance on the dot probe task despite the multitude of studies performe d to investigate the causes of attentional bias using variations of the task. As such, the purpose of the investigation was to model

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11 the dot probe task and its findings us ing a NN. The study further developed a probabilistic model (i.e., a BN) to define disc rete probabilistic relationships between the variables of the task. 1.7.1 Objectives of the Neural Network Model Multiple simulations with the NN model will be performed to investigate issues related to the dot probe sim ilar to the earlier works using the Stroop task (Cohen et al 1990; Matthews & Harley, 1994). Matthews and Harley (1996) investigated three potential causal mechanisms of attentional bias: exposure intensity and threat monitoring (explained above). Simulations in the current study investigated the first two of those causes vis--vis the dot probe task and an additional mechanism consistent with the interaction hypothesis Consistent with the hypotheses of Matthews and Harley, the current study proposed that repeated exposure to threat stimuli lead to an atte ntional bias towards such stimuli for the exposure condition. The intensity mechanism posited that individu als assigned a higher negative valence to a stimulus owing to higher levels of trait a nd state anxiety. The simulation attempted to model this mechanism in a NN. Simulation 1 was identical to the preceding simulation except that results will be presente d in terms of RT rather than activation levels and error of the network. In doing s o, I hoped to overcome a significant limitation of the Matthews and Harley model. Specificall y, they did not simulate the timecourse of psychological process. As such, the current study represents the first work to attempt to do so. The first simulation was aimed at replic ating the main empirica l findings of the dot probe task for each of the three mechanisms. Re sults were to be pres ented in terms of RT in ms computed from equations derived fr om the number of iterations required to produce the output, and the typical RT for th e condition. The main assumption in this

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12 case was that a linear relationship exists between the number of iterations required to produce the output and the typical RT specifi c to each condition. As such, we made a similar assumption to that of Cohen et al. (1990). 1.7.2 Objectives of the Bayesian Network Model The Bayesian network (BN) model served as a “proof of concept” of the advantages of probabilistic modeling in anal yzing data. The Bayesian model of the dot probe consisted of the following variables: 1. Anxiety level of the individual, entered as normalized scores on the STAI. 2. The arousal rating of the negative stimulus This parameter reflected the arousal value of the emotional stimulus presented to the individual. After the parameters were set, the arousal value was computed using the probabilistic relationships established for different valu es of the other variables. 3. The side on which the dot probe appeared specified simply as “same” or “opposite” for dots replacing the negative and neutral stimuli, respectively. 4. The direction of attention specified as either toward the negative stimulus or away from it. 5. The reaction time classified as fast and slow. The model was used to perform inference that is, find the probabilities of one or more of the variables being in a given state, given the knowledge of the states of all or some of the remaining variables. 1.8 Hypotheses A hypothesis was associated with each of the two models to be developed in the study: Empirical findings from existing of the dot probe studies can be simulated using a NN. Furthermore, a relationship does exist between the number of iterations required by the network to compute the output and the RT for the particular condition of the dot probe task. Finally, th e NN will be able to correctly simulate the various mechanisms of attentional bias.

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13 6. Quantifiable and discrete probabilistic rela tionships exist among the variables in the dot probe task that can be uncovered in the BN model.

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14 CHAPTER 2 REVIEW OF LITERATURE According to information on the website of the Anxiety Disorder Association of America (ADAA [ADAA, 2004]), anxiety diso rders (Generalized Anxiety Disorder (GAD), Posttraumatic Stress Disorder (PTSD) Panic Disorder, Obsessive Compulsive Disorder (OCD), Social Anxiety Disorder (SAD), and specific phobia affects) are the most common mental illnesses in the Unite d States, affecting 19.1 million adults (ages 18-54). Treatment of these disorders costs th e U.S. more than $42 billion annually, twice the amount spent on treatments for non-anxiet y related disorders, including physical illnesses (Simon, Ormel, Von Korff, & Barlow 1995). Indeed, prescription drugs for treatment of these illnesses are among the mo st commonly used in the world (Barlow, 2000). Of the various anxiety disorders, GAD, SAD and specific phobi a affects together afflict about 15.3 million indivi duals, or 10.9% of adult Americans. Further, GAD and phobia affects are twice as likel y to afflict women than me n. People suffering from some form of anxiety disorder are six times more likely to be hospitalized for a psychiatric treatment than non-sufferers. Clearly, an unde rstanding of the causes and mechanisms of how anxiety can lead to anxiety disorders is required so as to devise better treatment protocols. For ages, philosophers have linked anxiety to the very essence of being human (see Barlow, 2000), which is quite an ironic obser vation given that human s spend billions of dollars every year to rid them selves of the same. Anxiety an d anxiety disorders have been

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15 observed in various cultures, from the Eskimo hunters of Greenland in the early part of the last century, who experi enced a sudden and extreme pa nic attack on their hunting trips (Danish travelers to the region recorded it as “ kayak angst1”) and not be able to venture far out of the village again to a “sore neck” that affected the Khymer refugees in more recent times. Another consistency of these disorders is their prevalence among women. According to a WHO repor t, the odds of women being affected by some form of anxiety disorders are 1.63 (95% c onfidence interval) (Barlow, 2000). The aim of the current study is to devel op a Neural network (NN) and Bayesian network (BN) model of the dot probe task to investigate the underlying mechanisms. This chapter provides a review of literature related to attenti on, attentional biases, and PDP models developed to investigate the mechanis ms of attention. Th e chapter reviews the two PDP models of an attention task develope d so far, specifically a model of the classic Stroop task (Cohen, Dunbar, & McClelland, 1990) and a model of investigating the mechanisms of the emotional Stroop task (M atthews & Harley, 1996). Literature related to the dot probe paradigm is covered in significant detail to highlight methodology, variables, and salient characteristics of the task. 2.1 Anxiety Humans have a limited attentional capacity ; implying that in or der to efficiently perform multiple tasks simultaneously, it is crucia l to identify the task relevant cues and the level of detail to which each cue must be processed. The information processing system then must process these relevant cues in requisite detail a nd ignore the others; a job delegated to the attentional system As a re sult, the system plays a key role in survival 1 Panic attack experienced by Eskimo seal-hunters while hunting alone for days in their kayak. After the attack, the afflicted hunter could not venture but a few miles out of the village.

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16 and evolution (Mogg & Bradley, 1998a). Howeve r, the amount of attentional capacity available is affected by the em otional state of the person. Research over the last two decades ha s led to several robust findings linking anxiety to performance decrement on a broad range of tasks. Wood man and Hardy (2001) refer to anxiety being generally accepted to be an unpleasant emotion. Lang (2000) describes human emotions to have devel oped around two key motivational systems that play key roles in evolution and survival, na mely the appetitive and defensive systems. Emotions in general and anxiety in partic ular influence the selective attention and information processing capability of an individual. The general propensity of an individual to experience high a nxiety and the short-term anxiety he or she experiences in a particular situation are distinguished as trait anxiety and state anxiety respectively. However, trait anxiety does have a bearing on the level of state anxiety experienced by an individual; typically, individuals with trait anxiety have a tendency to experience higher levels of trait anxiety in stressful situations when compared to low trait anxious individuals (Williams, Watts, MacLeod & Matthews, 1988). 2.1.1 Measuring Anxiety Anxiety is mainly measured through paperand-pencil self-report questionnaires. One of the most frequently used scales to measur e levels of state and trait anxiety is the Spielberger’s State and Trait Anxiety I nventory (STAI) (Spiel berger, Gorsuch., & Lushene, 1970). The STAI has both a state ve rsion (STAI-S) and a trait version (STAIT); the state version is the mo st commonly used inventory to measure state anxiety. Both versions consist of 20 questi ons; the STAI-T consists requi res individuals to rate how they generally feel on a 4-point frequency sc ale (from 1 = almost never to 4 = almost always) while its state counterpart asks them to rate their feelings at that moment on a 4-

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17 point intensity scale (from 1= not at all to 4 = very much so). Maximum possible score on both versions is 40 while the minimum possible is 10. The test has been reported to have high internal consistency (Spielberger Gorsuch, Lushene, Vagg, & Jacobs, 1983). Other popular inventories include the Autonomic Perception Questionnairre (APQ) (Mandler, Mandler & Ur viller, 1958), the Af fective Adjective Checklist (AACL) (Zuckerman, 1960), and the Activation-De-activ ation Checklist (AD-CL) (Thayer, 1967). One drawback common to all self-report methods is the inability of the participants to accurately and reliably re port on their cognitive proce sses (Nisbett & Wilson, 1977). 2.1.2 Cognitive Models of Anxiety A number of cognitive models of attenti on and attentional biases have been put forward to explain the relationship between anxiety and attention. One key feature emerging from these models is that attenti onal bias is critical in the origin and maintenance of anxiety and emotional disorder s like GAD. Up until the latter part of the 1980’s, there were two main theories explai ning how anxiety affects attention, Beck’s cognitive theories of emotional disord ers (Beck, 1976; Beck, Rush, Shaw, & Emery, 1979; Beck, Emery & Greenberg, 1986) and Bower’s theories based on his network model (1981). Beck’s theories in particular, have been influential in devising new treatment protocols for depression and anxiety, specifically cognitive-behavioral therapy (Butler, Fennell, Robson, & Gelder, 1991; Simons, Murphy, Levine & Wetzel, 1986). Beck (1976) proposed that humans have set schema that they use to process the information. All incoming information pa sses through the schema, which attaches semantic meaning to it. In people sufferi ng from anxiety disorders, the schemata pertaining to processing thr eat or danger are dysfuncti onal, resulting in selective

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18 processing of schema-congruent information when activated. Similarly, depression is associated with dysfunctional schema ta related to loss or failure. Bower (1981) explained the same phenome non using an associative network of emotions and memories of events In such a network, emotions are connected to memories of relevant events (happy and sad) to form nodes of th e network. Activation can travel in either directi on; activating a particular emo tion node can trigger specific memories and vice versa. When activated, a node also activates, to some extent, the nodes connected to it. For instance, normally the node representing “sadness” is linked to nodes representing memories of sad events. Fe eling “sad” will trigger memories of sad events and thinking of these events will activate sorrow. This means that events are tagged with their emotional va lue before being stored in the network. In depression, events are tagged as negative more freque ntly and as having higher intensity of negativity. This increase in strength of c onnection between the memory nodes and the incoming information nodes implies that even events with low values of sadness have a higher negative impact on depressed individual s, as compared to normal individuals and also strengthen the connections more. Similarly, attentional bi as towards anxiety causes a tendency towards selective proc essing of negative or threat ening information, causing the individual to experience hi gher levels of anxiety. Both models explain the role of anxiet y in causing and main taining attentional biases. Overwhelming evidence exists in suppo rt of most of the pr edictions of both the above models (e.g., Clark & Teasdale, 1982; Bradley & Matthews, 1983; MacLeod et al., 1986). However, the models fail to explain some of the findings emerging from the studies on attentional biases. In particular, both models predict that both anxiety and

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19 depression should be associated with atten tional biases on all aspects on information processing, namely selective attention, reasoning, and memory (Mogg & Bradley, 1998a). However, studies have failed to uncove r any evidence either of an attentional bias towards threatening stimuli in depr ession (MacLeod et al., 1986) or of a recall (memory) bias in anxiety (Mogg, Matthe ws & Weinman, 1987). On the contrary, research suggests anxiety is linked to an at tentional bias towards threat while depression is associated with a memory bias to wards negative information (Mogg & Bradley, 1998a). Figure 2.1 Cognitive mechanisms underlying biases in initial orienting to threat in anxiety To explain these findings, Williams et al. (1988) proposed a new model relating attentional biases to anxiety and depression. To begin with, th ey associated anxiety with a tendency for preattentive vigilance for thre at and depression with a bias towards postattentive elaborative processes, thereby ex plaining the lack of a recall bias is anxiety and a similar lack of bias in preattentive processes in depression. The model proposes two mechanisms for directing preattentive and attentional bias towards threat stimuli in Resource Allocation Mechanism High trait anxiety: orient towards location of threat Low trait anxiety: shift attention away from threat. Stimulus input “State x Trait interaction” view (Williams, Watts, MacLeod, & Matthews, State Anxiety (mimics effect of high threat input) Trait anxiety determines whether processing resources are directed towards or away from a stimulus that has been judged to be threatening Affective Decision Mechanism High Threat No Threat

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20 high anxiety individuals; the Affective Deci sion Mechanism (ADM) evaluates the threat value of incoming stimuli and outputs the re sult into the Resource Allocation Mechanism (RAM) (Figure 2-1). The RAM allocates atte ntional resources towards or away from threat based on trait anxiety of the individual with high trait anxious individuals having a tendency to orient towards threat and low tr ait anxious people orie nting away from the same; this is the interaction hypothesis. As indicated in Figure 2.1, the difference between high and low anxious individua ls becomes more pronounced w ith an increase in the threat-value attached to the stimulus by the ADM. Consequently, the ADM can be thought of as a mechanism to assign priorities to incoming stimuli. Three main themes of the model are: 1. Anxiety is associated with di fferent patterns of selective attention rather than with detailed information processing. Cognitive bias for anxiety acts on the preattentive stage, looking for threatening stimuli in the environment. 2. Individuals who have a tendency to display an attentional bias towards threatening stimuli are more prone to anxiety and anxiety disorders under stress. 3. Trait anxiety influences the direction of the attentional bias, implying individuals with high trait anxiety are more likely to experience a higher level of state anxiety in more situations. Williams, Watts, MacLeod and Matthews ( 1997) revised their 1988 model within a connectionist framework Parallel Distribute d Processing model of Cohen et al. (1990). The revised model is explained following the review of PDP models of the Stroop task below. Recent theories of anxiety appear to complement the Williams et al. (1988) model. For example, Matthews (1990) proposed that emotions serve to assign processing priorities to incoming stimuli based on the vi ew of evolutionary functions of emotion (Oatley & Johnson-Laird, 1987). Eysenck (1992 ) devised the hypervigilance theory on

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21 the basis of the interaction hypothesis. He pr oposed that not only are high trait anxious people more biased towards attending to threat information (i.e., high specific hypervigilance) but they may attend to any task irrelevant stimuli wh en anxious (i.e., high general hypervigilance or dist ractibility). The theory furt her suggests that high trait anxiety results in a higher rate of environmental scanni ng, with the general focus of attention being very broad but becoming narro w when focusing on cue relevant stimuli. Eysenck and Calvo (1992) explained the e ffect of anxiety on selective attention and subsequently on performance with th e Processing Efficiency Theory (PET). According to the theory, processing of anxi ety-relevant stimuli increase demands on working memory, thereby reducing the amount of resources available to process task relevant information. Another possibility em erging from the PET is that performance decrement exhibited by high trait anxious individuals on experimental tasks in individuals occurs because they selectively attend to stimuli that are relevant to their anxiety and not to the task at hand. The PET is a formalization of the line of cognitive research being followed in the study of anxiety. Research emphasis has been to focus on the patterns of allocation of selective attention to tasks associated with high anxiety (Matthews & McLeod, 1994). The susceptibility of high anxious indivi duals to attentional bi as towards processing information relevant to their anxiety is a r obust finding and has been repeated in various situations with a host of different populations. The role of attentional bias in select ive attention has been explained using a searchlight analogy (Williams et al., 1997): Sel ective attention is likened to a searchlight beam, with the area illuminated by the beam as the center of attention. Some peripheral

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22 attention is devoted to information in the ar ea not illuminated direc tly by the searchlight. This information can cause an involuntary shift in attention causing attentional draining from the main task and thereby leading to de terioration in performan ce. Attentional bias is explained as an attentional vigilance to threat and has been projected as the main factor in causing and maintaining anxiety (Ma tthews, 1990; Eysenck, 1992). Bradley, Mogg, Falla, & Hamilton (1998, p. 737) explain this cycle: “Individuals with a tendency to adopt such a vigilant attentiona l style would be more likely to detect potential sources of danger in their environment, which in tu rn would exacerbate their anxious mood.” hman (1993; hman & Soares, 1993, 1994) reached similar conclusions from a different research perspective. They suggested that preattentive proc esses also regulate vulnerability to phobias with fear evoking stimuli working in much the same way as threat stimuli in anxiety. Specifically, fear re sponses to stimuli are initiated by automatic analysis mechanisms. These mechanisms are guided by biologically prepared threat stimuli and direct attention to the stimulus once it is analyzed. 2.2 Attentional Bias The above discussion reveals the importanc e of attentional bi as in evaluating incoming stimuli and directing attention. Williams et al. (1997) assume an attentional bias to have occurred when there is a discre te shift in attention to some change in the environment of the individual. They specify three assumptions regarding the shift in attention resulting from the bias esse ntial in studying at tentional biases: 4. The shift encompasses all sense modalities (vision, touch, taste, smell, etc) 5. Although usually passive and involuntary, the shift can be voluntar y (i.e., attention can be deliberately focused on the area). 6. Onset of the shift is brought about by a di screte change in the environment (i.e. by the onset or offset of some event).

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23 Researchers have used two basic paradigms to study attentional bi ases, interference methodologies (specifically, the dichotic listening paradigm and its visual analog, the Stroop task), and methods to test directly fo r attentional bias (nam ely, the visual search and dot probe paradigms). 2.2.1 Dichotic Listening Paradigm Mainly used in studying selec tive attention, the dichotic listening paradigm and its visual analog are now the l east preferred paradigms for st udying attentional biases. The basic version of the task cons ists of simultaneously playing a different audio message in the left and right ear of the subject using headphones. Participants are then asked to “shadow” (say out aloud) one of the messages as it is played. Early studies found participants could effectively follow only one of the messages, though some information (e.g. a high pitch tone, or cha nge from a male to female voice) from the unshadowed message still got through. The explanati on offered was that the messages were distinguished on the basis of some physical characteristics (e.g., pitch, amplitude, etc.). For a full review of theories of selective attention see (Abernethy, 2001). The paradigm was instrumental in establishing that attentional bias acts early in the information processing system. In the study of attentional bias using dichotic listen ing paradigm, the task was based on the premise that anxious individuals were more likely to attend to threat and other stimuli that directly re lated to their life ev ents. Parkinson and Rachman (1981) used the task to study lowered auditory thresholds in concerned mothers. They presented audio messages consisting of words representing pain and other unpleasant stimuli embedded at various volumes to two groups of mothers; those whom had children admitted to the hospital for some surgical procedure a nd a control group with no children admitted.

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24 Results indicated the experimental group identified more embedded words than the control group. The paradigm lost stature following a study on PTSD sufferers (Trandel & McNally, 1987), in which it failed to find any attentional bias in war veterans towards Vietnam-related words. Participants with and without PTSD experienced similar disruptions to all threatening stimuli; this was a major shortcoming since it does not allow the method to be made reliably sensitive to the specific fears of the population being studied. 2.2.2 Stroop Task The classic Stroop task (S troop, 1935) consists of di splaying names of colors written in different colored inks (Figure 2.2( a)) in which particip ants are required to either read the word or name the color of the ink as quickly as possible. The dependent measure in this case is the response time to name the color or read the word. Typically, participants are able to ignore the effects of ink colo r while reading the word aloud but experience significant interference with the wo rd when trying to name the color of the ink. Interference is greatest if the word is an antagonistic color-name (e.g., word “GREEN” printed in red ink (Figure 2.2(a)) or represents an antagonistic color (e.g. word “GRASS” printed in red ink) (Jensen and Rohwer, 1966, MacLeod, 1991). Meaningless stimuli (e.g., a row of X’s) do not interfere with the ink naming at all while congruent colors slightly facilitate na ming the color (“RED” printed in red ink [Figure 2.2(b)]). Various explanations have been pres ented for the observed discrepancy in response times for color-naming and word-r eading. The simplest one explained the observed interference on the basis of discre pancy in processing times required for the word reading and color naming. Researchers proposed that color naming is more

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25 automatic than word reading and so takes l onger to process than word reading, causing interference at the ou tput level. So, although both input s were detected simultaneously, response from word reading arrived at the ou tput level before its counterpart from the color-naming task. However, Glaser and Glaser (1982) put the explan ation to test and Figure 2.2 Versions of the Stroop task. proved it inadequate; they provided particip ants with advanced knowledge of the ink color by displaying a color patch of the same co lor as the color of the ink. Participants displayed interference effects even when the color patch was displayed 400 ms before the word. The effects came to be known as Stimulus Onset Asynchrony (SOA) effects. A more robust explanation was offere d by MacLeod and Dunbar (1988) on the basis of degree of automaticity of different ta sks. Numerous studies have established that automaticity on a task increas es by practice according to the power law (Kolers, 1976; Newell & Rosenbloom, 1981; Anderson, 1982; Logan, 1988). MacLeod and Dunbar (1988) reasoned that if amount of practice could make a ta sk more automatic, it would show up in appropriate changes in Stroop in terference with the mo re automatic task interfering with the performance on the less au tomatic one. To test the hypothesis, they trained individuals to associ ate four different shapes w ith four different colors. GREEN RED SPIDER a. Conflict condition, GREEN in red ink b. Congruent condition, GREEN in red ink c. Emotional Stroop for spider phobics, in red ink

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26 Participants were trained by presenting the sh ape in a neutral colo r (white) with each shape being presented 72 times. The same patte rn of training was car ried out daily for 20 days. At the end of the first day of traini ng, participants were ad ministered the Stroop task with the shape. On an average, part icipants were 100 ms slower at shape naming than at naming colors. The end of the fifth da y saw significant increases in speed of shape naming, with the shapes in terfering with color nami ng. By the time the study was completed (20 days of 72 trials per stimulus for a total of 2,520 trials per stimulus), participants displayed significant interferen ce with color naming and a small amount of facilitation in naming colors (evident from increased RT when the shape and color were conflicting and reduced RT when the shape a nd the color were congruent). On the other hand, colors showed very little effect on shape naming (shapes had taken the place of words and become the more automatic task). Word reading is considered an automatic task because indivi duals have arguably practiced it more than the more controlled a nd less practiced task of color naming. The theory has since been modified based on the findings of MacLeod and Dunbar (1988), who proposed that tasks have varying degrees of automaticity and control. Specifically, the degree of automaticity of tasks is a conti nuum rather than a dichotomy (i.e., tasks are not simply controlled and automatic but vary in their degree of automaticity or control, with some being more automatic than others ). For instance, if a study consists of two tasks with one being more automatic than the other, performance on the less automatic task will suffer due to interference from the more automatic process. The emotional version of the Stroop task us ed a negative affective word instead of a color name. Participants had to name the color of the negative word (words

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27 representing specific phobias for phobics). Fi gure 2.2(c) depicts a slide presented to a spider phobic. The emotional Stroop is an ad aptation of the classi c Stroop task that compares the response times of participants on color naming a series of emotional words as opposed to color-names (Matthews & Harley, 1996; Williams, Matthews & MacLeod, 1996). For anxiety, the affective word is ei ther threatening (e. g. “death”, “injury”, “sickness”) or non-threatening word (e.g. “chair”, “picture”). Individuals with high trait anxiety were hypothesized to di splay higher levels of interference in naming the ink color of a threatening word rather than a non-threatening wor d. Studies have found results congruent with the hypothesis. The first study using this paradigm was conducted on patients suffering from GAD (Matthews & MacLeod, 1985). They found the experimental group to be significantly slower at naming th e color of threat words. Similar results have since been observed in patients suffering from a host of different emotional and anxiety disorders, including Post traumatic stre ss disorder (PTSD) (Threas her, Dalgleish & Yule, 1994), obsessive compulsive disorder (OCD) (La vy, van Oppen & van den Hout, 1994), specific phobics (IAS, like social and spider phobics ) (Lavy, van den Hout & Arntz, 1993) and panic disorders (McNally, Amir, Louro, L ukach, Reimann & Calamari, 1994). One key finding apparent from studies with populati on groups suffering from different anxiety and emotional disorders was that individuals w ith these disorders exhibit the greatest difference in interference w ith the corresponding control grou ps when the valence words used represent threats relevant to their sp ecific condition. For exam ple, in a study with GAD patients worried about physical inju ry, Mogg, Matthews & Weinman (1989) found that participants displayed th e most interference when the word was related to physical

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28 danger (e.g. injury, fracture, etc.). Similarly, the greatest interferen ce effects for social phobics are induced by words representing socia lly threatening situations (Hope, Rapee, Heimberg, & Dombeck, 1990), and words of physic al threat cause the greatest influence for panic disorder patients (McNally, Am ir, Louro, Lukach, Reimann, & Calamari 1994). Researchers put forward different expl anations to account for the findings associated with the emotional Stroop task. One view was that anxious individuals allocate more attentional resources to threat words a nd process them in greater detail due to an attentional bias toward threat. The increase in resources consumed by processing threat information lead to the interference. A second explanation posits that threat words cause a spike in the level of stat e anxiety, disrupting performan ce on color-naming task. Some researchers (MacLeod, 1990; de Ruiter & Brosschot, 1994) questioned the validity of both the above explanations, stating that a te ndency to divert atte ntion from emotional cues can also lead to observed interference. The latter explanation was only the first of several criticisms levied agai nst the emotional Stroop task. One major drawback of the emotional St roop variations was in interpreting the results of the task; the task offered no eviden ce as to whether the interference occurred at the information processing stage or at the res ponse selection stage. Further, it failed to shed any light on the role of state and trait anxiety in the observed effects. Interpretative difficulties apart, the paradigm also lead to some unexpected results. Specifically, studies with phobics did not find any threat-related in terference when participants were in close proximity (physical or chronological) with thei r threat situation or object. For example, snake phobics in the presence of snakes (Ma tthews & Sebastian, 1993) and social phobics

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29 getting ready to give a speech right after testing (Amir, McNally, Reimann, & Clements, 1996) did not reveal expected interference effects for sn ake and threatening social situation related words. Finally, the task m easured only deteriorati on in performance due to attentional bias (Willams, et al., 1997). Ho wever, interpretative difficulties remain, by far, the more serious shortcoming of the task. 2.2.3 Dot Probe Task Interference paradigms like the dichotic listening paradi gm and the Stroop task failed to offer a direct indices of the mechan isms underlying attentional bias, as explained by the interpretative difficultie s encountered in the Stroop ta sk. Alternativ es to these tasks are the visual search paradigm and the dot probe paradigm. The dot probe is a direct measure of attentional bias experienced by individuals (Williams, et al., 1997). Developed by MacLeod, Matthews and Tata ( 1986), it was modified from paradigms in cognitive psychology that used response time to visual probes to assess attention (Posner, Snyder & Davidson, 1980; Navon & Margalit, 1983). These paradigms suggested that particip ants would respond faster to a pr obe stimulus when it appeared in an attended rather than unattend ed region of visual attention. The paradigm measures attentional drain due to existing biases in attention without confounds of response selection by measuring the reaction time of a neutral response (button click) to a neutral stimulus (dot-pr obe). The basic steps (F igure 2.3) consist of simultaneously displaying an emotional cue (w ord or picture) paired with a neutral cue for a short duration of time (traditionally 500 ms though other times have been used). Following cue offset, a dot appears in the spatial location of one of the two cues. Participants are instructed either to indicate the position of the probe (probe position task, i.e., indicate whether the probe appears on the le ft or right, or top or bottom by pressing

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30 the appropriate button) or indi cate its type (probe classificat ion task; two different probes are used, say the letters ‘E’ and ‘F’, and participants are requir ed to indicate the letter) as quickly as possible. The driv ing hypothesis for the MacLeod task (another name for the dot probe used in literature) was that high anxiet y individuals systematically attend to threat-related stimuli and this would be reflected by faster response times to probes replacing emotional cues as opposed to non-th reatening cues and al so response times of non-anxious individuals for the same cues. 2.2.3.1 Initial studies (basic dot probe task) The first dot probe study (MacLeod, et al ., 1986) used the paradigm to measure attentional bias in GAD patients. Sixteen in dividuals diagnosed with GAD and referred for anxiety management by their practitioner were tested against a group of sixteen low anxiety (LA) controls. The GAD group obtai ned mean scores of 44.7 and 52.5 on the Figure 2.3 Illustration of th e dot probe paradigm state and trait versions of the STAI while the LA group scored 36.3 and 39.5, respectively. On the Beck Depression Inde x (BDI), GAD sufferers and controls groups CHAIR BLEED 1. Fixation cross appears for a fixed duration (typically 500 ms) 3. Dot probe appears in the spatial location occupied by one of the stimuli immediately following the offset of the stimuli. 2. Stimuli appear (arranged either vertically or horizontally) time CHAIR BLEED

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31 scored 13.9 and 7.6, respectively, with GAD patie nts being significantly more depressed than their LA counterparts (the significant di fference in the depression levels of the two groups added a confound that was later rem oved by testing a low-anxious depressed sample against controls). Patients were matche d with controls for age, gender and verbal intelligence (measured by the Mill Hill Synonyms Test). Each group was shown a total of 288 word-pairs on a computer monitor; 48 cons isted of a threat word paired with a neutral word while the remaining 240 were a pair of neutral words. Of the threat words, half represented physical threat while th e other half represented social-threat. Words were displayed centered on the ve rtical axis of a VDU (Visual Display Unit), separated by a distance of 3 cm from each other (constituting a visual angle of less than 2 degrees), for 500 ms. Participants were instructed to read out loud the word appearing on the top in every trial and to press a button as quickl y as possible when a probe appeared to indicate its presence. The probe (a white dot that appeared with equal probability in the spatial location of one of the two words) appeared in 96 trials and remained on the screen until participants pr essed a button to indicate its presence. All threat-neutral pairs (48 in al l) were followed by the probe while the other 48 probed trials consisted of filler items chosen at random from the neutral pairs. Trials could thus be classified into three types; probed-threat, probed-neutral, a nd unprobed-neutrals. On trials without the probes, the next picture was displayed followi ng a delay of one second. Results confirmed the hypothesized preferenti al attention to threat information by the GAD group and an avoidance of the same displayed by controls. When the probe appeared at the top, the GAD group was significantly fast er at responding when it followed a threat word (593 ms) than a ne utral word (652 ms). The same trend was

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32 observed for probes appearing in the lower s ection of the screen, with the high anxiety group responding faster when the probe was preceded by a threat word (663 ms) than when it followed a neutral word (695 ms). Reaction times for the control group followed the reverse trend, with controls reacting fast er to probes replacing neutral words than threat words, implying an avoidance of th reat cues. Specifically, controls recorded reaction times of 540 ms when the probe replaced a threat word in the upper area vs. 524 ms when it replaced a neutral word in the same location; for probes appearing in the lower area of the display, controls were 32 ms faster in responding to probes following neutral words (584 ms) as compared to threat words (616 ms). The study was among the first to offer an ex planation for atten tional bias towards threat stimuli without any confound from respons e bias (as would have been the case if Stroop task had been used) of the results. Re sults from this and ot her dot probe studies were critical in formulation of important assu mptions regarding the na ture of attentional bias. Williams et al. (1997) acknowledged the contribution of the paradigm as, It [the MacLeod et al. (1986) study] showed that we needed to assume the existence of a decision mechanism which (a) was at a preattentive level, (b) was sensitive to general differences in threat, (c) allocated attention to di fferent parts or aspects of the environment, and (d) was independent of response bias (Williams, et al. 1997, p. 83) In a subsequent study using the para digm, Broadbent a nd Broadbent (1988) attempted to answer some of the questions emerging from MacLeod et al. (1986). They investigated whether preferen tial allocation of attention to threat stimuli was a characteristic of only clinically anxious peopl e or if people with sub clinical levels of anxiety also display a similar bias. Further, they questioned whether the effects were a function of the personality of the individual (and therefore pe rmanent) or more a function

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33 of the state of the individua l regardless of personality characteristics (and so more fleeting). Making a few minor changes to the setup of MacLeod et al. (1986), they tested a total of 104 women in four diffe rent experimental setups to answer the above questions. In each experiment, they divided the wome n into a HA group and a LA group based on their STAI scores. Individuals scoring greater than 35 on the trait form of the STAI were classified as HA while those scoring less than that were classified as LA. Results confirmed the existence of a simila r bias in the sub-anxious sample and an avoidance of threat information by the LA group. On the whole, HA participants responded faster when probes appeared in pla ce of threat stimuli as opposed to when the probe replaced the neutral stimulus in the th reat-neutral pair while the reverse was true for LA participants. When threat words appeared in the upper area, HA individuals responded faster to probes repl acing the threat word (587 ms) th an to probes that replaced the neutral word in the threat -neutral pair (637 ms). Similarly, when the probe and the threat word, both appeared on the bottom, the HA group took 650 ms to press the button while taking 667 ms when the word appeared on the bottom and the probe appeared on top. Opposite readings were observed for th e LA group; individuals were slower to respond to probe appearing in the location of the threat word (RT 656 ms and 678 ms for probes and threat words on the top and bottom, respectively), while reacting faster to probes that replaced the neutral word in the thre at-neutral pair (649 ms for threat word in upper position and probe in lower and 657 ms for the opposite). They also found trait anxiety a more reliable indicator of attentional biases as co mpared to state anxiety; high trait anxious participants in their study c onsistently displayed similar patterns of

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34 attentional bias while the effect of state anxiety differed from one experiment to the other. Around the same time, MacLeod and Ma tthews (1988) ran a follow-up study to investigate the effects of state and trait anxi ety on attentional bias es. They tested 36 high and low trait anxious (non-clinical) college students for attentional biases towards exam related cues under conditions of low stress (12 weeks before the exam) and under high stress (one week before the exam). Here ag ain the STAI (trait) score (dividing median score 39.5) was used to stratify the student s into high and low anxious categories. Participants were presented 288 word pairs, 96 of which were pr obed. The probed pairs consisted of an equal number of threat and ne utral pairs. Half the threat words used in this case were related to examinations while the other half were general threat words chosen from earlier studies. Words were rated for threat value and pertinence to examinations on a scale of 1-5 (1 being th e least and 5 the maximum on both scales) by eight independent judges and both groups of threat words ha d the same threat rating (4.1). Authors computed the atten tional bias score to analy ze the results by subtracting the mean RT when the probe occurs in the same place as the threat word from the mean RT when the probe and the threat cue occur in different locations. Attentional Bias = 2 ) / / ( ) / / ( LT LP UT LP UT UP LT UP UP = Upper Probe, UT = Upper Threat LP = Lower Probe, LT = Lower Threat Positive values of bias score signified vigilance of threat and negative values indicated avoidance of threat. Attentional bias scores were used to obtain a single index of probe and threat positions so as to simp lify computing a four-way interaction of trait

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35 anxiety, test time, threat position and probe position. Resu lts revealed a tendency to attend to threat stimuli in general by the high trait anxi ous group and avoidance by the low trait anxious group. Exam words did not a ttract much attention from either group in the first test but did so in the second. Also both groups reco rded equivalent increases in state anxiety but with opposite effects. The HA group respon ded even faster when the probe and threat appeared in the same lo cation while the low a nxious group recorded shorter latencies to probes repl acing the neutral word in critical pairs. This pattern of change could not be explained on the basis of trait anxiety alone and lead the authors to infer that the patterns were in fact due to an interaction of state and trait anxiety. Researchers later referred to this pattern of attention allocation and the effect of state and trait anxieties on it as the interaction hypothesis (Williams et al., 1988). The dot probe has proved to be an effec tive measure of attention allocation and preattentive bias to different kinds of stim uli. Studies have repl icated the task and confirmed the existence of similar patterns of attention allocation in several different samples. Different studies e ffected changes in the task methodology, making the task more sensitive to the sample being studied. One shortcoming with early versions of the task was due to probing in only a portion of th e trials. This limited the amount of data that could be collected. Also, because each th reat word was probed, the appearance of such a pair could act to prime participants fo r the probe and hence result in a faster RT. Mogg, Bradley and Williams (1995) disposed of this requirement by probing participants at the end of every trial and in structing them to indicate the position of the probe (top or bottom for cues displayed cen tered on the vertical axis) by pressing the appropriate button. Trials on which the threat -word, neutral word pairs were displayed

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36 came to be known as critical trials. Using this methodology also rendered the requirement of reading aloud the top word infeasible, eliminating another confound. One potential flaw of probing in every tria l was the possibility of partic ipants adopting a strategy to attend to the spatial location of one word onl y (and press the button indicating presence of the probe depending on whether the probe a ppeared on the side they were attending to or not). MacLeod and Chong (1999) overcame this potential pitfa ll with the “forced reaction time” version of the task. Essentially, they used two different probes (two dots in vertical and horizon tal orientation ‘:’ and ‘..’) and participants were instructed to perform probe classification, pressing a different key depending on the type of probe used. One criticism the basic dot probe shared with the Stroop was that it too provided only a snapshot of attention at the instant of probe onset. Specifi cally, both tasks only provide a definite answer of the direction of attention when the dot probe appeared, but no information to the direction of attention allocation prior or subsequent to the probe. Three explanations have been offered to account for the observations of the dot probe. First is the vigilance-avoi dance pattern of processing (Mogg, Matthews and Weinman, 1987; Williams et al., 1988), which says anxious individuals follow a pattern of first attending to and then avoiding the threat cue in an effort to mitigate their anxious state. Such a pattern may also act to maintain their anxiety-state by preventing anxious individuals from habituating to threatening events. A second possibili ty, consistent with the models of Beck (1976) and Bower (1981) is that anxious individuals orient themselves toward threat and subsequently have trouble disengaging at tention. To answer these questions required modifying the task of MacLeod et al. to measure the time course of attention.

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37 2.2.3.2 Manipulation of stimulus duration Mogg, Bradley, de Bono and Painter (1997) modified the task to measure attention at three different times by manipulating stimul us duration. They presented 192 word pairs (96 threat-neutral and 96 ne utral-neutral pairs) to 35 volunteers in top-and-bottom orientation, and displayed each word pair randomly for 100 ms, 500 ms or 1500 ms. The first condition was designed to be shorter than the inter-saccadic interval during active visual search (varies between 200-300 ms: Ko wler, 1995) and therefor e did not allow any shifts in attention. On the other extreme, 1500 ms allowed for detailed processing of the stimuli and multiple overt shif ts in attention. The 500 ms condition represented the most frequently employed time period for the dot prob e. They also varied the inter-stimulus period randomly among 750, 1000 and 1250 ms. Th reat words consisted of an equal number of words referring to social threats (e.g., stupid, despised, criticism) and physical threat (e.g., illness, injury, fracture). Word-pairs in critical trials were ordered such that there was an equal probability of the type of threat-word di splayed (social, physical), its location (top, bottom) and the probe position (t op, bottom). Participants’ emotional states were assessed after they completed the task by having them fill out the STAI, BDI, and Social Desirability Scale, among others, and were divided into tw o groups (high and low state anxiety) based on their STAI-state scor es (dividing median score 30) for analysis. After removing outliers from the data (trial s with high error rates and RT more than three standard deviations from the mean), Mogg et al. (1997) th ey found a significant main effect for exposure in that individuals tended to respond faster to probes in the 100 ms duration (485 ms) as opposed to the other two conditions (latencies of 498 ms and 503 ms for 500 ms and 1500 ms conditions) regard less of trait anxiety. High state anxious individuals showed a signifi cant trend to respond to thr eat, recording response times10

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38 ms faster to probes replaci ng threat words (mean 493 ms) than those replacing neutral words (503 ms). On the other hand, low anxi ety scorers displayed a non-significant effect of threat-avoidance, with RT for threat words 8 ms slower than for neutral words (502 ms and 494 ms, respectively). Bias scores for the high state anxiety group were 10, 9, and 11 and –11, -10 and –1 for the low state a nxiety group for the 100, 500 and 1500 ms conditions respectively. Post hoc analysis revealed significan t difference in bias scores averages over the three condi tions for the two groups, with significant differences in the 100 ms condition and non-significant tr ends between the other two. Findings did not support the vigilance-avoi dance hypothesis, that is, there was no significant difference of attentional bias with display duration. According to the vigilance-avoidance hypothesis, dysphoric individua ls have an initial attentional bias towards threat cues, which puts them in an aggr avated state of fear. In order to escape this state, they direct attention away from the stimuli. The authors refrained from making any generalizations on the basis of this study, as it was the first in the field, and offered two explanations for the observations; first, they suggested that approach-avoidance could be more likely a characteristic of individuals with anxiety disorders (GAD, panic disorder, etc.) rather than those with sub clinical anxiety, and secondly, they suggested that attentional avoidance could be influenced by the relative threat value of the stimulus. 2.2.3.3 Backward masking Backward masking of stimuli was a technique used in the Stroop task to restrict awareness and measure strictly preattentive bias toward s threat cues. It involved displaying the word for a very short time (e.g ., 14 ms) and then replacing it with a lengthmatched mask (random characters). The mask wo rked to prevent detailed processing of the word and thus strictly measured pre-a ttentional bias. The same was adapted for the

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39 dot probe. All word pairs were displayed for a very short duration (typically 14 ms), and then covered by a mask (consisting of random letters or symbols, one for each letter of the word, or contortions of th e letters of the words themselves) for a similar duration. The probe followed stimulus-offset and part icipants were required to perform probe position or probe classification task. The hypothesis for the masked dot probe remained virtually unchanged from the basic version; HA individuals were predicted to attend to the spatial location formerly occupied by the mask covering the threat word. Results of studies using this version of the dot probe confirmed th e hypothesis with HA individuals and those with GAD (Bradley, Mogg & Lee, 1997b; Mogg et al., 1997). A barrier in generalizing findings from the above st udies and other dot probe studies using single words as threat stimuli is the amount of threat information that single words can convey. As noted by Bradley et al. (1997a) and Mogg et al. (1997), single words convey a limited amount threat-infor mation and, once that information is extracted, the word loses part or all of its threat value. Additi onally, a potential confound exists due to the threat value and relative frequency of use of threat words as HA individuals use threat words more often more than LA individuals. Finally, research suggests that attentional biases are guided by innate, evolution-driven mechanisms; words do not fulfill the criteria fit of ecologi cally valid threat stimuli (LeDoux, 1995). An alternative to single words is using photogr aphs of threat stimuli (mutilated bodies, attacking animals, angry faces). Pictorial cues are a much more ecologically valid threat cue than single threat words. 2.2.3.4 Pictorial dot probe task Bradley and his colleagues (Bradley, M ogg, Millar, Bonham-Carter, Fergusson, Jenkins, & Parr, 1997) designed a pictorial dot probe task, using pict ures rather than

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40 words as the emotional stimuli. They displaye d pictures of faces with happy, threatening or neutral expressions for 500 ms to a samp le consisting of subclinical HA students (grouped according to scores obtained in the upper and lower tertile s of the Fear of Negative Evaluation scale (FNE; Watson & Fr iend, 1969)). On critical trials, an emotional face was paired with a neutral face and participants were required to indicate the position of the dot. Results did not indicate a relationshi p between social anxiety and attentional bias but post-hoc te sts revealed a tendency of dysphoric individuals to avoid the threatening faces. Some later studies used genera l threat pictures rather than emotional faces. In one such study, Bradley, Mogg, Falla & Hamilton (1998) used pictures that were either severe (e.g., assault victims, mutilated bodi es) or moderate (e.g., man behind bars, soldiers) in threat value based on evaluation by j udges. Critical trials were the same as the preceding study, displaying a threat picture pa ired with a neutral photograph, displayed side by side for 500 ms. Results showed that HA participants were quicker to react to probes replacing higher rather th an moderate threat pictures implying a greater vigilance for higher threat cues. In a s ubsequent study, Mogg et al. ( 1998) employed pictures from the International Affective Picture System (IAPS; Lang Bradley & Cuthbert, 1995) and reached the same conclusions. The same authors (Mogg & Bradley, 1999) repeated the study using probe classification rather than probe position. Probe classification produced three times as many errors as probe position, and participants were slower by approximately 200 ms in responding the probes. Mean response times fo r probe position are in the order of 300400 ms and 500-600 ms for probe classifica tion (Mogg et. al, 1998, Mogg & Bradley,

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41 1998b). However, results still provided more evidence in favor of an attentional bias towards threat stimuli. Using the pictorial dot probe offered other options to measure the time course of attentional allocation and bias. An additional means to gain insight regarding direction of attention was the addition of tracking eye-movement to the basic task. One such study was undertaken by Bradley, Mogg and Millar (2000); they added eye tracking to the basic dot probe task using pict ures of happy, threatening an d neutral facial expressions displayed for 500 ms. Gaze tracking measured “overt” shifts in attention, that is, voluntary shifts in attention, while reaction time to probes provided a measure of covert orienting of attenti on (involuntary shifts). Dysphori c individuals were faster in responding to probes replacing threatening stimu li and eye tracking patterns revealed that they also tended to initially orient to the threat stimuli as opposed to non-dysphoric individuals. A masked version of the pictorial dot probe has also been developed (Mogg & Bradley, 1999), as have studies to inve stigate the time cour se of attention by manipulating stimulus duration. Bradley et al (1998 a) investigated the time course of attentional processes and found HA individuals displayed higher vigilance towards threat faces (but not towards emotional faces in ge neral) when the stimuli were displayed for 500 ms and 1250 ms. A substantial amount of research using dot probe has been conducted on removing the uncertainty surrounding information proces sing biases in social anxiety (review by Heinrichs & Hoffmanm, 2001). Some studies on this topic have suggested vigilance for social-threat cues while othe rs have found avoidance, partly due to the difference in

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42 methodologies of the studies. Early studies using social-threat wo rds did not reveal a clear relationship between social anxiety and attentional biases Asmundsen and Stein (1994) were the first to inve stigate this relationship usi ng social phobics. They used a modified version of the dot probe; displayi ng word pairs in topand-bottom orientation for 500 ms and instructing part icipants to read aloud the top word in every trial. Following stimulus offset, participants were to respond as quickly as possible to probe onset by pressing the appropriate button indicating probe positi on. Results indicated that social phobics responded quicker to the probe regardless of probe location when the social threat word appeared on the top. Thus, although the study proved that social phobics selectively attend to socially evalua tive words, it suffered from interpretative problems due to the aforementioned decrease in RT regardless of probe position. As such the results could also be interpreted as i ndividuals displaying enha nced vigilance after reading a threat word. Two other studies w ith similar populations also resulted in no significant effects towards social threat cu es by socially anxious people (Horenstein & Segui, 1997; Sanz, 1997). 2.2.3.5 Social anxiety Mansell, Clark, Ehlers and Chen (1999) tested socially anxious individuals under conditions of socially evaluati ve threat and no-threat. Par ticipants were divided into groups on the basis of their social anxiety sc ores (lower (<8) a nd upper quartile (>17) scores on the FNE, respectively). Conditions of social threat were induced by informing participants that they were to give a speech to a live audience after the test. An equal number of participants were tested under thr eat and no-threat conditions. Stimuli in this case consisted of pictures of faces (happy, thre at and neutral) paired with a picture of a household object. The threat condition indu ced attention away from emotional faces

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43 ( both positive and negative) while the no-threat condition did not find any differences in attentional bias between the test and contro l groups. The authors also covaried out the differences in trait anxiety and depression indices and found an attentional avoidance effect. The fact that social phobics avoid em otional faces stimuli while other phobics (see below) direct attention to emotional stimu li lead the authors to suggest that phobics exhibit attentional bias es in directions which reduce th e uncertainty around the threat stimuli. For instance, findings for individua ls with high social anxiety have not been consistent with those obtained from various other groups afflicted by anxiety disorders and phobias. Lavy and van den Hout (1993) found a similar attentiona l bias for spider related words and pictures with spider-phobics which according to Mansell et al. (1999) was the best way for individuals to reduce unc ertainty about the spider. A social phobic, on the other hand, breaks eye contact by looki ng away from the face cue to achieve the same end result. However, a later study by th e same authors (Mansell, Ehlers, Clark, & Chen, 2002) using threat words as the salient stimuli with high and low socially anxious college students under conditions of social th reat and no-threat di d not find any bias towards or away from the threatening stimuli. Using pictorial stimuli, Mogg & Bradley (2004) examined social phobics for bias to threat cues and the time course of their attentional processes. Pictures of emotional facial expressions served as the emotional cue and were displayed for either 500 ms or 1250 ms. A significant trend to attend to pref erentially to negative faces as opposed to positive or neutral faces was observed for the clinical population in the 500 ms condition. In the 1250 ms condition however, no bias was f ound for either the clinical or the control group.

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44 2.2.3.6 Drug abuse Lubman, Mogg and Bradley (2000) compared methadone-sustained drug users to age-matched controls for attentional bias towards drug-related cues. Participants were shown drug-related pictures (needles, spoons, heroin wraps, etc.) paired with neutral pictures for 500 ms. The hypothe sis predicted the existence of a drug related bias as posited by some cognitive theories (Robins on & Berridge, 1993); consequently relapse has been linked to an attentional bias towa rds drug related stimuli (Wikler, 1965; Siegel, 1979; Stewart et al., 1984; Childress et al., 1986; Baker et al., 1987; Tiffany, 1990). Findings supported the prediction in that opiate drug users di splayed an attentional bias towards drug related information. 2.2.3.7 Smoking and alcoholism The same theories incited research for at tentional bias in smokers and alcoholics towards their respective drugs. Townsend a nd Duka (2001) extended the research of Lubman et al. (2000) and adapted it to inve stigate for a bias in non-dependent heavy social drinkers towards alcohol-related cues as opposed to occasional social drinkers. Critical trials consisted of an alcohol-related cue (word or pi cture) paired with a neutral non-alcoholic cue. All cues we re displayed for 500 ms. Resu lts confirmed a bias towards alcohol related cues in the h eavy drinker group. Ehrman et al. (2002) based their research on the two studies mentioned above and exam ined whether current cigarette smokers displayed an attentional bi as towards smoking cues as opposed to non-smokers and former smokers, respectively. They found sm okers to have a signi ficantly higher bias towards smoking cues than non-smokers while former smokers had an intermediate level of bias.

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45 2.2.3.8 Eating disorders The cognitive model of Vituosek and her colleagues (Vitousek & Holon, 1990; Vitousek & Orimoto, 1993) id entifies two basic cognitive factors to blame for causing and maintaining eating disorders; individua ls’ body image (shape and weight) and the schema biased processing of the body image. Clearly, the second factor is reminiscent of the models of Beck (1976) and Bower ( 1981). Earlier studies on body image and eating disorders relied heavily on data mainly collected through self -report questionnaires. Using self-report measures is potentia lly limiting because it may be confounded by distortions of self-image a nd denial (Fairburn et al. 1991; Vitousek & Orimoto, 1993). The dot probe, on the other hand, can provi de an objective measure of attention and response to food cues. Following this line of reasoning, Reiger, Schotte, Touyz, Beumont, Griffiths and Russell (1998) examined the existence of a bias toward body and shape related stimulus words in patients of anorexia nervosa, bulimia nervosa, and controls. They used words reflecting large or thin physiques paired with neutral words on critical trials. Individuals w ith eating disorders exhibited a bias towards words describing a large physique and away from neutral words and words representing a thin physique. Taken together, these results may indicate that individuals with eat ing disorders process information related to fatness while ignoring information related to thinness. If so, it could indicate a fear of a ttaining a large physique despit e evidence to the contrary, explaining why patients of these eating disorders show an aversion to food. In yet another study, Placanica and her asso ciates (Placanica, Faunce, Soames Job, 2002) tested high and low scorers on the Eating Disorder Inventory-2 (EDI-2) under fasting and non-fasting conditi ons for bias towards food stimuli. They found a bias towards high-calorie foods under the fasting condition across all participants while high

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46 EDI-2 scorers showed a bias to low-calorie (non-fat) foods only when not fasting. This hunger-driven bias towards high-calorie foods may shed some light on the binge-purge and cycle found in bulimic-nervosa. 2.2.3.9 Pain and miscellaneous areas Some other non-traditional ar eas where the dot probe has been applied of late include attentional bias towards pain stim uli (Keogh et al, 2001; Dehgani, Sharpe & Nicholas, 2003) in chronic pain sufferers, towards words related to Irritable Bowel Syndrome (IBS) for IBS sufferers (IBS; Gutie rrez, 2001), to sexual and violent words in victims of sexual trauma (Bush, 2000). 2.2.3.10 Limitations of the dot probe Although it has been used with considerable success in various studies with a host of anxiety and other disorders, the dot pr obe task has several limitations. The most glaring insufficiency of the task is that it does not provide a complete picture of the timecourse of attention but only of a ttention at the instant of probing. One of the more serious criticisms of th e task, and one it shar es with the Stroop task is that the salient stimuli are presente d in the foveal region. Although foveal vision and attention are not the same, it is believe d that it is impossible not to attend to information presented within a 1-degree radius of fixation. Thus, resu lts of the two tasks cannot conclusively say whethe r threatening stimu li attract attention or hold it once they are detected. However, the task is easy to administer and provides a direct reading of attentional bias at the instant of probing. 2.3 Connectionist Models of Attention Williams et al., (1997) identified two ma in issues concerning the study of attentional biases: the cause and the mech anism. Causes refer to the reasons why

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47 attentional biases manifest themselves only in some people under certain conditions. Mechanisms refer to the point in the inform ation processing system at which they act. The first issue has been addressed by different paradigms used to st udy attentional biases. For example, robust relationships have been established between trait anxiety, state anxiety, stress and their affect on attentional biases using th e dichotic listening paradigm, the Stroop and dot probe tasks. Studying mech anisms, on the other hand, has not been as straightforward. Developing a clear understand ing of the mechanisms is important to understand attentional biases more thoroughly and devise more effective treatments for the various disorders. An attractive method to study mechanisms of various constructs is through computer simulations. Developing such a simu lation allows researchers to intervene, change variables and measure their effect. Ne ural Networks (NN) models (also known as Parallel Distributed Processing (PDP) mode ls) are computational modeling paradigms based brain operations and are the prefe rred modeling paradigm when simulating attentional biases on computers. In fact W illiams et al. revised their 1988 model in 1997 to explain in PDP models (Williams et al., 1997). The second analysis tool employed in th e current study is a Bayesian belief network, or Bayesian network (BN) for shor t. BN are probabilistic graphical models. The current study represents the first known attempt to use BN to arrive at probabilistic relationships between variables involved in the dot probe task. Current popular applications of these models are in the fi elds of mainstream computer science (e.g., dataminingdiscovering relations hips between relationships from data, expert diagnostic systems, etc.) and business and finance (e.g ., risk analysis for insurance and other

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48 projects, stock market prediction). Bayesian networks’ application to cognitive reasoning has been rather limited, mainly said to be more suited to higher or der reasoning tasks than simulating lower, automatic processing ta sks. One of their most widely known applications is in the sometimes annoying Microsoft Office Helper and troubleshooter. BN are most applicable in areas where rela tionships between variab les are known (this is explained below). BN also offer an intu itive method of modeling the relationships graphically. The current study w ill use BN to develop a causa l model of attentional bias as per the dot probe task and then fine-tune the probabilistic rela tionships between the variables. In this section, the ba sics of the main NN mode ls developed for studying attentional bias, the models to simulate the Stroop task by Cohen et al. (1990) and the extension of the same to the emotional Stroop by Matthews and Harley (1996) are summarized. The section first explains the th eory and working of NN. The two models are then discussed in detail. The theory and working of BN are explained next along with an example of how they will be applied in the current study. 2.3.1 Neural Networks A neural network is a massively parallel distributed processor made up of simple processing units, which has a natural prope nsity for storing ex periential knowledge and making it available for use. It re sembles the brain in two respects: Knowledge is acquired by the network from its environment through a learning process. Interneuron connectio n strengths, known as synaptic we ights, are used to store the acquired knowledge. (Haykin,1998, p.2) 2.3.1.1 Overview A NN consists of a number of small proces sing elements that are also referred to as neurons Each neuron is capable of perf orming only very simple calculations;

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49 computing the input and using a transfer or activation function to compute an output. A single neuron in the human brain is much slower than a microprocessor (by about an order of 106, with a neuron taking 10-3 s per operation compared to the 10-9 s of a microprocessor). The brain overcomes this disadvantage of speed by using parallel processing. Each neuron is connected to numerous other neurons, with the connections between them known as synapses allowing simultaneous para llel activation of varying neural circuits. Shepherd and Koch (1990) es timated the number of neurons in the brain at 10 billion with 60 trillion synapses. As such, NN try to emulate this natural parallelism. Each synapse has a strength associated with it; referred to as the “ interneuron connection strengths or synaptic weights ” (Haykin, 1998, p.2). Each uni ts’ input is a summation of the weighted output of all the ot her active units that project to it. Synaptic weights can be positive (excitatory) or negative (inhibitory). Clearly, these weights are the most basic variable in a NN; they are adjusted accord ing to the application area of the NN using a learning algorithm 2.3.1.2 Learning Learning in a NN is the process of adjus ting the synaptic weights according to the variations in the learning data (i.e., th e problem). Indeed, learning paradigms are classified into learning with a teacher ( supervised learning ) and learning without a teacher ( reinforcement and unsupervised learning ) (Haykin, 1998). In supervised learning, for example, the NN is provided w ith an input and the known result for that input (called target output ). The network computes the out put based on the input (called computed output ) and compares it against the target output. The weights are adjusted using a function to minimize the error betw een the target and computed outputs. A detailed explanation of supervis ed learning is provided in the next section. Alternatively,

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50 when learning without a teacher, the netw ork uses one of two techniques: (1) reinforcement learning, where the NN has an in-built “critic” (some scalar index of performance) and learns by mini mizing the scalar index or (2) unsupervised learning which, instead of a critic has a task independent measure that optimizes the free parameters of the network. Specifically, in unsupervised learning, the network uses the task independent measure to find statistical regularities in the input data enabling it to form internal representation of data to automatically derive new classes of data (Becker, 1991). For a full discussion on supervised and un supervised learning, see (Haykin, 1998). 2.3.1.3 Supervised learning. Supervised learning consists of two ph ases, a training phase followed by a test phase. The training phase consists four steps th at culminate in the network being able to compute the correct output for each of the input cases. The steps are: 1. Input data with known outputs ( target outputs ) to the network. 2. Allow the network to compute its output ( computed output ) based on the given input. 3. Compute the difference between the computed output and the target output. 4. Use the learning algorithm to adjust the s ynaptic weights based on the magnitude of the error difference. The test phase supplies new inputs no t previously seen by the network. 2.3.1.4 An example of supervised learning. An example of supervised learning is a model to predict whether it will rain on a particular day or not. The first step is to identify the independent and dependent variables in the model and choose the NN architecture2 for the problem. In this example, the inputs 2 Architecture of a NN refers to ho w the neurons in the network are connected to each other. Three basic architectures are single-layer f eedforward networks, multi-layer feed forward networks and recurrent networks. Multi-layer feedforward network architecture is the one most commonly used in supervised learning including in the current study and in the simulation of the Stroop (Cohen, et al. 1990) and the

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51 are the four of the most basi c variables known to affect weat her on a given day, pressure, humidity, temperature, and wi nd-direction. The output consis ts of two nodes, rain or norain; signaled by activat ion of the respective nodes. The ne xt step is to initialize the network by assigning weights to the inter-n euron connections. To start with, these weights may be generated randomly within some range. Once the network is initialized, it must be trained, constituting the third step. Input for the training phase consists of the four input variables and the value of the observed ( target ) output for a given day (i.e., whether it rained or not). The training pha se involves the network computing the output for a large number of training input cases, and adjusting the synaptic weights accordingly until the computed output matches the targ et output for each case. The successful completion of all four steps culminates in th e network being ready to predict whether or not it will rain on a given da y given the temperature, pr essure, humidity and winddirection for that day. 2.3.2 Details and Theory 2.3.2.1 Overview Figure 2.4 shows a basic multi-layer feedfo rward NN (multi-layer refers to multiple layers of weights) that uses the back-p ropagation algorithm for learning (also known as the backpropagation network (BPN) or the backpropagation architecture. The BPN consists of an input layer, one or more hidden layers and one output layer. Figure 2.4 provides an example of a network th at contains an input layer of two nodes (I1 and I2), one hidden layer of four nodes (H1 through H4) and one output layer of two nodes (O1 and O2). Input and output neurons are always in one of two states, firing emotional Stroop (Matthews & Harley, 1994). For detailed information on network architectures see Haykin (1994).

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52 (active) or not-firing (inactive), whereas hi dden neurons, can have a discrete output or use the activation level itself as the output for the node (explained in detail below). Input to the network is provided by applying an act ivation pattern over the input nodes. Output of the network is given by activation of one of the output nodes. The network has one input unit for each input of the problem be ing modeled, and one output unit for each possible output (e.g., the NN in the weather exam ple in the previous section contains four input variables and two output variables). Th e number of hidden layers and the number of units in each layer is also problem specific, but typically the number is between the number of input nodes and the number of output nodes; lesser than the number of input units and greater than the number of output units (Blum, 1992). Hidden nodes provide non-linearity to the network. A BPN is considered fully connected if every neuron in one layer is connected to every neuron in the next layer. Figure 2.4 is an example of a fully connected BPN. When the neurons in one layer are onl y connected to certain neurons in the next layer, the BPN is considered partially connected In either case, there are no connections between neurons in the same layer.

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53 Figure 2.4 A general multi-layer backpropagation neural network. 2.3.2.2 Notation This section describes a notation based th at used by Haykin (1998) to clearly refer to weights on any connection in any of the wei ght layers and to refer to any unit an any of the three layers of units. As mentioned earli er, a NN consists of la yers of units (input, hidden and output). Weights are denoted by wn ij which is the weight w on the nth layer of weights between nodes i and j (note that nodes i and j are in different layers of units for instance, the input and hidden or hidden a nd output layers). For example, the NN of Figure 2.4 consists of two layers of weights; the first (denoted by w1) between the layer of input units and the hidden la yer and the second (denoted by w2) between the hidden and output layers. Therefore the wei ght of the connection between the first unit in the input layer and the third unit in the hidden layer is denoted by w1 13 Similarly, the weight w1 11 w1 13w1 12w1 14 Input Layer Hidden La y e r Output La y e r H1 I1I2H4O1O2 H2H3w2 11 w1 24 w1 21w1 22w1 23w2 12w2 21w2 22w2 31w2 32w2 41w2 42 1s t Weight Layer ( w1) 2n d Weight Layer ( w2)

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54 on the connection between the second unit in the hidden layer unit and the first output unit is denoted by w2 21. Input to a unit (not show n) is denoted by the letter x ; so xj represents the input to the jth unit in a layer. Activation level of the unit is denoted by a so aj denotes the activation level of the jth neuron. 2.3.2.3 Initialization The network can be initialized by rando mly assigning randomly generated weights to the connections between units. Alternativ ely, the designer can assign weights to the connections according to the problem. In eith er case, the weights are adjusted according to the problem domain using the learni ng algorithm during the training phase. 2.3.2.4 Node Details Figure 2.5 is a detailed repres entation of a node of the network of Figure 2.4. The figure refers to the third node in the hidden la yer of the network; receiving input from the two input units ( I1 and I2) and transmitting the result to th e two output units (not shown). As illustrated, the processing unit performs two basic tasks: 1. Computes the net input (denoted by x3 with the computa tions performed by the summation unit ). 2. Computes the activation level from the net input (denoted by a3, using the transfer function to perform the computations). Output of the node may or may not be the same as the activation level. 2.3.2.5 Net input The net input to a hidden unit is typically the sum of the product of the output of each input unit and the synaptic weight of the connection between the two. Sometimes a bias value ( b ) may be added to the net input of each node to lend

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55 Figure 2.5 Details of a simple pro cessing unit of a neural network. variability to the network. The bias can be a constant set by the experimenter so it is the same for every node, or a random number ge nerated from within a specified range. Therefore in this case, the net input is: b w I w I x 1 23 2 1 13 1 3 --2.1 where I1 and I2 are the outputs of the input un its. The above equation can be generalized to give the net input for any arbitrary node (jth node of the nth layer) as: b w a xi n ij i j --2.2 where ai is the activation of the units in the previous layer. 2.3.2.6 Activation level Computing the activation level consists of applying the transfer (activation) function to the net input. A BPN requires the transfer function to be non-linear, Summation Unit Transfer Function 3r d Processing Unit of Hidden Layer 1s t Weights Layer Input Layer w1 23 w1 13 I1 I2 f bias b x3+ba3

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56 continuous and monotonous (i.e., differentiable at any point of the curve) (Haykin, 1998; se also Cohen, et al. 1988). A class of func tions known as sigmoid functions fulfills these requirements and the function that is most commonly chosen as the activation function among the functions of this class is the logistic function given by: Figure 2.6 Graph of the logistic sigmoid function jx j je a x f Activation 1 1 ) ( --2.3 Figure 2.6 depicts the graph for the logistic function of equation 2.3. Note that the slope of the function is the highest when the net input is zero and increases more slowly the higher the value of activation. 2.3.2.7 Output As mentioned above, the output of the node depends on whether the node is a hidden or output node. For a hidden node, the out put of the node is usually the same as the activation level. Howeve r, a threshold value is se t for output nodes (by the experimenter) and the node fires if and only if the activation level of the node exceeds the 0 12 3 4 5 -5 -4 -3 -2 -1 0.0 0.2 0.4 0.6 0.8 1.0 Net Input

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57 set threshold. Alternatively, the output ma y be selected as some function based on the activation level of an individual unit or all the units in the output layer. The number of output units of the network depends on th e problem being modele d and the number of units that can be active simultaneously depends on the problem parameters. In short, The network loops until an output is obtained (i.e ., one of the nodes fires). Cohen et al. (1990) used one such function in their model; the pr ocess is explained in the next section. 2.3.2.8 Training During training, the NN is supplied with the target output for each input pattern. The network computes the output (comput ed output) and the learning algorithm compares the computed output with the target output to calculate the error. The learning algorithm used in the two simulations of the Stroop task is known as the delta rule. Errorinformation is then propagated back thr ough the network and each unit of the network adjusts the weights of its c onnections according to some error-minimizing function (e.g., gradient-descent, so called because the function estimat es the direction in which to move down the slope of the function to as to mi nimize the function). Error correction may be carried out after each of the Figure 2.7 shows the flow of computa tion and weight-correction for a BPN. Backpropagation algorithm is by far the most popular error driven learning algorithm. Summarizing, the training phase consists of the following steps: Activate the appropriate input units. Compute the output. The network is allowe d to run until one of the output units fires. Compute the error (difference between the computed and target outputs). Propagate the error information backwards through the network to all units

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58 Figure 2.7 Flow of activation (solid lines) and error (dotted lines) in a multi-layer backpropagation neural network. and adjust the synaptic-weights using the b ackpropagation algorithm. Error correction may be performed after a single input activation is presented to the network; or after all the input patterns have been pr esented to the NN. In the latt er case, the network performs the corrections based on the total error (the mean-squared-error [see Haykin, 1998]) for all input patterns, which is the square root of the mean of su m of the squares of error for each input pattern. Mathematically, n error error error msen 2 2 2 2 1... --2.4 The network performs error-correction until the error falls within the specified limit set according the problem. I1I2O1O2 Input Layer Hidden La y e r Output La y e r 1s t Weight Layer ( w1) 2n d Weight Layer ( w2) Error computation

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59 2.3.2.9 Testing Once the training is complete, the netw ork is ready to accept new inputs (as opposed to the training data) and produce an output. 2.4 Connectionist Models of the Stroop Task Two PDP models of the Stroop task have been developed to date, the first by Cohen et al. (1990) that simula ted the findings of the basic Stroop task and the second, a simulation of the emotional Stroop, repor ted by Matthews and Harley (1996). This section discusses the design of both networks along with issues concerning training and testing of the two. In order to be considered a successful simulation of the Stroop task, a model must replicate the main em pirical findings of the task. Word reading is faster than color naming. Mean time to read a color word is 350450 ms while naming a color patch of a ro w of X’s takes about 200 ms more (550650 ms) (Dyer, 1973; Glaser & Glaser, 1982). Word reading is not affected by color ink. Color of the word to be read has virtually no affect on the time to read the word. Words can influence color naming. Content of the word interferes with color naming; conflicting words cause a substa ntial increase (varia ble but commonly 100 ms) in the RT to name colors. Conversely, congruent words faci litate performance in color naming, reducing RT by 20 ms (Regan, 1978) to 50 ms (Kahneman & Chajczyk, 1983). Facilitation is less than interference. Although congruent stimuli have been used only sparsely, general findings are consiste nt with the pattern mentioned above in that the amount of facilita tion (20 ms) is much less than interference (100 ms). 2.4.1 The Cohen Model Cohen et al. (1990) used a partially connected PDP model to simulate the Stroop task (Figure 2.8). The model produced the ma in empirical findings of the Stroop task. Input to the network consisted of specifying the task and task parameters (i.e., whether to

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60 perform color naming or word reading and the ink color and the word). Output consisted of generating the response for the input through activation of the correct ink color for the color-naming task and the correct word fo r the word-reading task. The Cohen model computed the time course of a psychological process by presenting results in terms of reaction time (RT), computed by deriving a linear relationship between the number of iterations taken by the network to compute the output and typical RT for the task. As such, the authors required the network to mimic the variability in reaction times of human participants performing the St roop task. This mandated some changes to be made in the way each unit computes input and the selec tion of the final output by the network. 2.4.1.1 Structure Cohen et al. (1990) used a partially connected BPN, consisting of two processing pathways, one for color naming and one for word reading. Each of the pathways can be thought of as a distinct neural network with both competing for the final output, achieved by connecting the hidden layer to both out put units (see Figure 2.8). The network contained six input units to specify ink colo r, task and the words to be read, and two output units representing the po ssible outputs (i.e., red or gr een). The model could handle only two words, “Red” and “Green”, prin ted in two possible ink colors, RED and GREEN. Inputs were presented as a pattern of activation over th e input nodes. 2.4.1.2 Initialization Cohen et al. (1990) assigned small, random weights to the conn ections between the hidden and input layers and inte rmediate values (either +2 or –2) to connections between the input and hidden layers. In the latter case, values were chosen to obtain a straightforward mapping from the i nput layer to the hidden layer.

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61 Figure 2.8. Neural network model fo r simulation of the Stroop task 2.4.1.3 Net input Each unit computed net input in a simila r manner to the one described in equation 2.2. Two changes were made to the manner in which net input was computed for each unit; the first was to allow the network to simulate the time course of a psychological process. The initial change was based on the cascade models (McClelland, 1979), which also simulated the time course of psychological processes; ne t input at any instant of time t was defined as the running average of its net input over ti me. Mathematically: ) 1 ( ) 1 ( ) ( ) ( t x t x t xj j j --2.5 where, is a rate constant and, Input layer Hidden layer Output layer 1s t Weights layer 2n d Weights layer “red” “green” red green Color Naming Word Reading RESPONSE TASK DEMAND GREEN RED INK COLOR WORD READING H1 H2H3H4 O1O2I1 I2I3I4I5I6 w1 11 w1 12 w1 21w1 22w1 31w1 32w1 64w1 63w1 43w1 44 w1 53 w1 54

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62 i ij i jb w t a t x ) ( ) ( --2.6 Note that equation 2.6 is the sa me as equation 2.2 except that ai( t ) is the activation at time t Additionally, using this function guarant eed that the network would always reach a stable asymptotic state and result in an output. The second change was made to add variab ility of performance to the network; a normally distributed random bias was associated with each hidden and output unit and added to the net input (denoted by b in equation 2.6). 2.4.1.4 Activation The logistic function (equati on 2.3), applied to the net input computed according to equation 2.6, was used to compute the activation. Mathematically, ) (1 1 ) ( )) ( ( ,t x j jje t a t x f Activation --2.7 Again, note the only difference between e quation 2.7 and equation 2.3 is in the value of the net input. 2.4.1.5 Output Output of the network was indicated in the same way as a typical BPN, by the firing of an output node (i.e., “r ed” if the node representing “r ed” fired and “green” if the other node fired). Cohen et al (1990) introduced variability in this step by making the firing of the output unit dependent on the re sult of a random walk (Link, 1975) or diffusion process (Ratcliff, 1978). Adaptation of these processes to computing the output of the network consisted of associating ev idence accumulators with each of the output units. The accumulators were set at 0 at the beginning of each trial and a small amount of evidence was added at the end of each tim e step; evidence added was random and

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63 normally distributed with mean based on the difference between the activation of the unit and activation of the most active alte rnative and fixed standard deviation ( = 0.1). So for the ith output unit, the mean i is given by )) max( (j i i ia a --2.8 is the rate of accumulation of evidence a nd was set at 0.1 through all their trials. The threshold was set at 1.0 for the evid ence; so the output unit fired when the evidence associated with a unit exceeded 1.0. 2.4.1.6 Training One difference between training the Str oop model and the weather example cited earlier was that the training in this case was completed separately on the word reading and color naming tasks, rather than both tasks at the same time. An input pattern consisted of the ink color or the word and the task to be performed. So an input for the color-naming task with color “red” was represented by “RED-COLOR-NULL”, activating the input un it for color “red” and the task demand unit (TDU) for “COLOR NAMING” only. The target output in this ca se was “red”. The network was then allowed to reach an asymptotic level of activation a nd generate an output and correct the weight in accordance with the error between th e computed and target outputs using the backpropagation algorithm. The Cohen model differed from a typical BPN in initializing and updating the weights. Firstly, connections in the first laye r were randomly assigned values of either +2 or –2. Secondly, weights on the connections between the TDUs and the intermediate units were kept constant (and not allowed to be changed during tr aining) so that the

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64 activation of the TDU did not provide any ex tra information to the intermediate units. However, the authors suggested th at these could be learned. One training objective was to make word reading more automatic than color naming, achieved by training the network on te n times as many word-reading stimuli than color naming stimuli, allowing it to strength en the word-reading connections much more than color-naming ones. Table 2.1 lists all the training patterns. Table 2.1: Input patterns and corresponding outputs used fo r training the network by Cohen et al. (1990) 2.4.1.7 Testing Testing involved providing all inputs for the task (color, word and task) to the network and allowing it to cycle through until th e output reached an asymptotic value. In all, the network was tested on 12 different inpu t patterns (listed in Ta ble 2.1) representing every possible condition, for both color-naming and word-reading. The conditions tested were congruent (word same as color), conflic t (different word and color) and control (only the color or the word depending on whet her testing is for color naming or word reading). A conflict condition of naming ink color for the word “Green” printed in “Red” ink was presented to the network as ac tivation pattern “RED -COLOR-GREEN” (i.e., activating nodes representing ink color “red ”, word “green” and color naming TDU). Cohen et al. (1990) recorded the number of iterations it took the network to reach an Ink color (Input) Word (Input) Task Condition Output Red RED WORD READING Congruent RED Green GREEN WORD READING Congruent GREEN Red GREEN WORD READING Incongruent GREEN Green RED WORD READING Incongruent RED Red GREEN COLOR NAMING Congruent RED Green RED COLOR NAMING Congruent GREEN Red RED COLOR NAMING Incongruent RED Green GREEN COLOR NAMING Incongruent GREEN

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65 asymptotic activation of the output units and used it to derive a relationship between the number of iterations and the reaction time by comparing the number of iterations against established reaction times for each condition. Naturally, this meant the relationship between the number of iterations and RT wa s dependent on the task being simulated. 2.4.1.8 Simulations and results Cohen et al. (1990) performe d six different simulations to test findings of the Stroop task in four different categories and explained those in terms of the PDP model. The four categories were: 1. Strength of processing which primarily explai ned the main empirical findings of the Stroop task on th e basis of connection strengths. 2. Stimulus onset asynchrony (SOA) effects, which investigated observing interference even when the ink color was displayed before the actual word. This simulation was the only one not in agreement with actual data. Specifically, the model displayed some influence of colo r on word reading when the color is presented early. 3. Practice effects: The simulation was base d on the study conducted by MacLeod and Dunbar (1988) who trained in dividuals to associate shapes with colors, creating a novel task which the i ndividuals had not practiced before. The Stroop task was then constructed in which individuals were presented with shapes in different colors and were required to name color the shape was originally associated with. Results indicated that pr actice on associating colors with shapes increased performance on color naming the shapes in the Stroop task consistent with the Power law. Simulation of this task included two different simulations which investigated the Power law and pr actice in the Stroop task and developing automaticity with practice. The first of th e two simulations plotted RT as a function of number of training trials (N) and found performance of the network increased on color naming the shapes according to the Power law. 4. Allocation of attention: The final two simulations tested the affect of attention allocation to performance on th e two tasks. Researchers have proposed somewhat opposing views on attention allo cation and its affects on performance. Some researchers define automatic tasks as requiring absolutely no attention (Posner & Snyder, 1975; Shiffrin & Schneider 1977), going so far as saying lack of attention should not influence performan ce on such tasks (Posner & Snyder, 1975), while others have challenged this claim, saying few, if any, processes can function without attention (Kahneman & Treisman,, 1984; Logan, 1980).

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66 Cohen et al. addressed the issue with thei r model. In the first of two simulations, they performed the two tasks on their model w ith varying degrees of attention allocation (activation of the TDUs) and found that color naming required more attention than word reading to maintain a given level of performance. More importantly, however, performance on both tasks degraded by reduced attention. In the second of the two simulations, the authors investigated respons e-set effects. More specifically, they evaluated whether words and objects that are not part of the response set cause significantly less interference than those that are (e.g., the word BLUE is never a correct response in the current simulation and so is not a part of the response set). The authors successfully simulated the picture-naming ta sk (Dunbar, 1985) and observed significantly less interference for words that were not part of the response set. Williams et al. (1997) updated their earlier model (Williams et al., 1988) within a PDP framework following the simulations by Cohen et al. (1990). They reconceptualized the ADM as the input units, assigned the task of tagging input with a threat value and the RAM as the TDU. Despite these revisions, their core assumptions of the interaction between st ate and trait anxiety remained virtually unchanged. Matthews and Harley (1996) built upon th e model of Cohen and colleagues (1990) by adapting it to simulate the emotional Str oop. However, their focus was on trying to explain the cause of attentiona l bias, and as such they we re not concerned with adding variability to their model. 2.4.2 The Matthews and Harley Model Matthews and Harley (1996) extended the Cohen model by applying it to the emotional Stroop task. The authors set realisti c objectives for the simulations, keeping in mind the lack of simulations and other inves tigations into the mechanisms of the task.

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67 Their main objective was to investigate three different mechanisms for generating attentional bias (exposure, intensity and attentional), based on different explanations of attentional biases. Simulating the emoti onal Stroop involved cha nging the network to present emotional words as inputs. Also, th e network was not designed to simulate the time course of attention, that is, in contrast to the work of Cohen et al. (1990), Matthews Harley (1996) did not present results by comp aring RT but compared relative activation of the output units. Details are expl ained in the sections below. 2.4.2.1 Hypotheses As stated, the model tested three qualitatively different explanations for attentional biases. The first, known as the exposure hypothe sis, proposed that repeated exposure to emotional stimuli lead to an attentional bias towards emotional stimuli causing an anxious person to be more practiced, and therefore more automatic, in reacting to emotional stimuli. The intensity hypothesis was second viable al ternative, and expl ained the basis of attentional biases as distressed individuals pe rceiving the same emotional stimuli as more potent (higher intensity) than normal individu als, and therefore placing a higher priority on processing that information. The hypothesis was further branched into state and trait portions, with high state anxiet y individuals perceiving higher intensity only during test conditions while high trait anxiet y individuals felt the same (hi gher) intensity all the time. The third hypothesis stemmed from Matth ews and Wells (1995) explanation of observed interference in the Str oop task. They suggested that attentional bias occurs due to a coping strategy adopted by distressed indi viduals to monitor potential sources of threat. Arguably, the coping strategy leads su ch individuals to pa y more attention to

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68 emotional stimuli, which in turn causes la rger interference effects. This called for activation of the task demand unit during testing. 2.4.2.2 Structure Matthews and Harley (1996) followed an evolutionary approach, extending the Cohen model for the emotional Stroop. After two unsuccessful architectures (Figure 2.9 (a)) that did not yield satisfact ory results for standard Stroop interference, they arrived at the final model (Figure 2.9 (b)). The first m odel was a straightforward extension of the Cohen model, while the final architecture featured extra connec tions as well as an additional TDU to monitor threat. The final model had nine input units, six hidden units, and five output units. As can be seen from Figure 2.9, input units represent semantic features of the word rather than the word itself. So each word was presented as activation of a unique combination of input units, and the network was trained to output the word corresponding to the semantic units activated. Color indica ted a color word and color type indicated the degree of redness, thus by ac tivating both the units simultaneously word “red” was represented. “Monster” is asso ciated with a large object (being) and negative emotion and therefore is presented to the network by th e activation of (large ) SIZE and (negative) EMOTION. The semantic codes words for all the words used by the network as seen by the output produced are listed in Table 2.2. Presenting i nput in this manner had two distinct advantages; firstly, it was consistent with psycholinguistic theories stating speech processing is a two level process. Secondly, it allowed the network to learn semantic similarities between words.

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69 2.4.2.3 Initialization The network was initialized using the sa me as the initialization method used by Cohen et al. (1990). 2.4.2.4 Input Since the network was not intended to mode l the RT of the psychological process, Matthews and Harley used the basic BPN equa tions to compute net input (equation 2.2) and activation (2.3) for each unit. 2.4.2.5 Output Obtaining output was rather straightforward in this case, given that the output produced in the first iteration of the networ k became the final output and was used for comparisons against ba seline conditions. 2.4.2.6 Training and testing Differences in architecture apart, both ne tworks implemented the BPN architecture and were trained using the same basic algor ithm. Presenting all training patterns to the network is called an epoch. Matthews and Harley trained the network for 400 epochs (i.e., cycling 400 times through all the traini ng patterns shown in Table 2.2). The number of training patterns of each type used for training and the activati on values depended on the hypothesis. Training patterns for the baseli ne condition are displayed in Table 2.2. The table highlights an interesting distinc tion in the training approaches for the two networks; the Matthews and Harl ey network was trained to ig nore input in the absence of a task specification, that is, when a TDU was not activated. Otherwise, Matthews and Harley still used Cohen et al.’s (1990) approach to make word reading more automatic than color-naming, training the ne twork more on word reading than color

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70 Figure 2.9 Matthews and Harley Model (a) the first two models. The dotted lines were connected in Model 2 while non-existent in model 1, (b) model 3 shared the same connections for the 2nd weight layer with model 1. Connections that differ in layer 1 are shown as solid li nes while those carrying over from 1 and 2 are shown in dotted lines. ‘Red’ ‘Green’ Color Color type Emotion Size Color Naming Word Reading H1 H2 H3H4H5H6 RED GREEN SPIDER HOUSE MONSTER ‘Red’ ‘Green’ Color Color type Emotion Size Color Naming Word Reading H1 H2 H3H4H5RED GREEN SPIDER HOUSE MONSTER Threat Monitoring H6 b. Final Model a. Models 1 and 2

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71 naming. Results were obtained by comparing the activations of th e output unit for each hypothesis condition against baseline activatio ns. The authors manipulated training sets for each of the hypotheses. Exposure condition involved doubling (chosen arbitrarily) the Table 2.2: Training patterns and number of times each condition was presented to the network to train for the emotional Stroop task. number of training patterns of emotional wo rd reading. To train for the intensity condition, Matthews and Harley changed the input from 1 to 8 fo r appropriate units, simulating hypersensitivity to the stimuli. Fi nally, attentional manipul ations did not entail any changes in training but the unit was set to a low positive (0.3) value during testing. The input patterns for which no output is listed were used to train the network to produce an output only if a TDU was activated. Stimulus Input TDU Activated Output Repetitions Color + Color Type Word Reading Red 16 Color Word Reading Green 16 Emotion Word Reading Spider 16 Size Word Reading House 16 Emotion + Size Word Reading Monster 16 Color + Color Type 2 Color 2 Emotion 2 Size 2 Emotion + Size 2 “Red” Color Naming RED 1 “Green” Color Naming GREEN 1 “Red” + Emotion Color Naming RED 1 “Green” + Emotion Color Naming GREEN 1 “Red” + Size Color Naming RED 1 “Green” + Size Color Naming GREEN 1 “Red” + Emotion + Size Color Naming RED 1 “Green” + Emotion + Size Color Naming GREEN 1 “Red” 2 “Green” 2 Color + Color Type Threat Monitoring Unit 2 Color Threat Monitoring Unit 2 Emotion Threat Monitoring Unit Spider 2 Size Threat Monitoring Unit 2 Emotion + Size Threat Monitoring Unit Monster 2

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72 2.4.2.7 Results The three test mechanisms tested in th is simulation are stated above, namely exposure, intensity and attention mechanisms. The first condition was further divided into two parts, emotion word exposure and emotion task exposure. The former simulated performance on the two tasks after increased exposure (presen ting the appropriate patterns 32 times as opposed to 16 during training) to reading emotional words. Results found an increase in reading emotional words while almost no effect was observed for color naming. The latter condition trained the network to respond to emotional words only when the TMU was activated, indicating an acknowledgement of the threat value of the word. This manipulation resulted in a marginal impairment of color naming and a similar improvement in word reading. However, the TMU was not activated during testing. In intensity manipulations, the researchers trained the network to simulate chronic hypervigilance to threat words by increasing the activation of the threat words from 1 to 8, resulting in stronger em otional Stroop interference but impaired performance on reading emotional words. The final condition tested performance while attending to the em otional content of the words for the tasks (word reading and color naming). The TMU was set to a low positive value (0.3) while testing to simulate co ncurrent attention to the threat value of the word, resulting in a significant increase in interference in color naming emotional words coupled with a small impairment the same for neutral words. The same manipulation resulted in a minor impairme nt of reading neutral words while having almost no effect on reading color words. All re sults were consistent with the findings of

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73 emotional Stroop interference having a sm aller magnitude than standard Stroop interference. 2.4.3 Pros and cons of using PDP models Although computational models in general, and PDP models in particular are attractive methods to simulate human beha vior, to understand underlying mechanisms, they are not without advantag es and potential pitfalls. O’ Reilly and Munakata (2000) summarized the major advantages and disadvantages of using PDP models. 2.4.3.1 Advantages 1. Models can aid in understanding phenomen a and their mechanisms. For example, the Cohen, et al. NN explained some findi ngs of the Stroop task in terms of the weights on the connections between units. 2. Models deal with complexity explaining phenomena that would be impossible to explain verbally. 3. Models are explicit. Models force re searchers to think clearly about the assumptions made in the models. Further, the results obtained from these models are clear and cannot be written off as some other processes interfering in the main task. An example is the lack of confor mity between the results obtained for SOA effects in the Cohen model. 4. Models allow control. Different variable s can be assigned different values, using different activation functions and so on. 2.4.3.2 Criticisms 1. Models are too simple. Models have to si mplify a lot of the variables in the task. Further, usually models involve only th e variables used in the tasks and no extraneous variables are modeled. They do not model the biological and physical variables in any detail. 2. Models are too complex. Some researcher s believe that models are too complex to be useful in explaining their behavior This is especially true for NN, although it is clear at an abstract level that the connections between the units in different layers are strengthened, th ey do not really provide an explanation of what the intermediate units represent. In essence, NN follow a black box approach to modeling.

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74 3. Models can do anything. Given enough da ta, PDP models can be trained to simulate just about any condition, which is analogous to a theory that explains everything. 2.5 A Belief Network Model of Attentional Bias in Dot Probe Paradigm Neural networks are founded in theories of neuroscience and mimic the architecture of the brain; so they offer an intuitive way to simulate attention and analyze its underlying processes. One limitation of such models however, is their “black box” approach, meaning that although one has access to the synaptic weights, interpreting their values is not straightforward. Questions sti ll abound regarding the ro le of the hidden units and meaning of the weights on synapses connected them. For example, both models of the Stroop task discussed above (Cohen et al., 1990; Matthews & Harley, 1996) list the weights on the connections between input and hidden units and between hidden and input units and how they are strengthened or weakened depending on the training data. However, hidden units do not represent discre te variables; theref ore knowledge of the connection strength cannot be interpreted in terms of a relationship between input and output variables.3 Further, as mentioned earlier, research into the causes and mechanisms of attentional biases have yielde d very consistent and robust re lationships between different variables of attention and the paradigm used to test it. However, no studies attempting to quantify the said relationships have been found. The current study attempts to do just that; determine probabilistic (or belief) values of variab les involved in attentional biases from the dot probe perspective. 3 As an illustration, consider the fact that the model of the Stroop task could have been implemented using a fully connected BPN as opposed to th e partially connected ones that th e authors used. In light of this evidence, what is the significance of the conn ections and the weights on those connections.

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75 A Bayesian network (or belief network (BN)) is a tool that allows simple and elegant modeling of a system with known variables and esta blished relationships. A BN is a graphical model that encodes probabil istic relationships among a set of variables (Heckerman, 1996). Graphical models are a marriage between probability theory and graph theory. They provide a natural tool for dealing with two problems th at occur throughout applied mathematics and engineering -un certainty and complexity -and in particular they are playing an increasingl y important role in the design and analysis of machine learni ng algorithms. Fundamental to the idea of a graphical model is the notion of modular ity -a complex system is built by combining simpler parts. Probability theory provides the glue whereby the parts are combined, ensuring that the system as a whole is c onsistent, and providing ways to interface models to data. The graph theoretic side of graphical models provides both an intuitively appealing interface by which humans can model highly-interacting sets of variables as well as a data structure t hat lends itself naturally to the design of efficient general-purpose algorithms (Jordan, 1988) Clearly, understanding BN requires an understanding of the basic laws of probability and graph theory, both of which ar e explained in the sections that follow. 2.5.1 Nothing is Certain Logic provides the tools for reasoning with absolutely certain values, like “if it rains, the grass will be wet”. Such a statement d eals with absolute certainty, that is, if it is known that it is raining, the grass will be wet. Logical reasoning, however does not work well with uncertain events. Consider the prob lem of trying to pred ict whether or not it will rain given that it is cloudy. Two uncerta in variables complicate prediction in this case: the state of cloudiness (e.g., the number and type of clouds) and the probability of rain given the state of cloudiness. Is the st atement, “if it is cloudy, it will rain” an absolute certainty? If the nu mber of mistakes made by the National Weather Service considered, the clear answer is “no.” Weathe r prediction has to deal with uncertainties; statements like, “if it is cloudy, it will probably rain.” The same is the case with the vast

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76 majority of contexts as few real world probl ems have absolute certainties associated with them. Statements like “you will fail the course because of your laziness”, or “reckless driving causes accidents” (from Pearl, 2000, p.1) reflect some amount of uncertainty. Surely not all lazy people fail the course, and not all instances of reckless driving result in accidents. What these statements imply is th at the particular actions mentioned increase the likelihood (or probability) of the consequence. The goal is to compute the probability in each case. Probability implies doubt, lack of regular ity, exceptionality. In other words, it is a measure of uncertainty. Logical reasoning of fers four different logical connectives, namely conjunction (“both the grass and the pavement are wet”), disjunction (“either the grass is wet or it is not”), implication (“if it rains, then the grass will get wet”), and negation (“the grass is not wet”). Combining two statements can lead to an inference about an event not explicitly specified; for example, combining “if it rains, then the grass will get wet” and “the grass is not wet” lead to the conclusion that it did not rain (Jensen, 2000). Probabilistic reasoning warra nts development of a simila r set of rules on the lines of logical operators to combine probabilistic values. For instance, to compute the probability of rain when the probability of “rain when cloudy” is 0.8 and the probability of “cloudy” is 0.7 requires developing a me thod to combine the two probabilities to arrive at the required one. Another question that begs to be answered is “how does one know the probabilities in the first place?”. There are two ways of computing the probabilities. The traditional approach, called the frequentist approach, bases the probability of an event on the frequency of prior occurrences of the same event. Perhaps the simplest example is

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77 computing the probability of getting “tails” in a fair-coin toss; the probability is based on the number of times the coin landed on tails in an arbitrary number (say 100) of trials. Clearly, the approach lacks applicability to many real world problems. The alternative is to assign belief values to the event, called the subjectivist or Bayesian4 approach, “according to which probabilities encode degrees of belief about events in the world and data are used to strengthen, update or weaken those degrees of belief. In this formalism, degrees of belief are assigned to propositions (sentences that take on true or false values) in some language, and those degrees of belie f are combined and manipulated according to the rules of probability calculus.” (Pearl, 2000 (p.2)). Two characteristics of belief values are worth noting. First, such values are assigned based on some degree of belief the experimenter has in the occurrence of the particular event and not on the frequency of the same. S econd, they are governed by the laws of probability. Using the second charac teristic, experimenters change the degree of belief assigned to different vari ables so that the assigned belief values are consistent with the laws of probability. The next section explains the basic axioms of probability theory. Subsequent sections build on the same la ws and explain their application to BN. 2.5.2 Axioms of Probability Probability calculus defi nes three basic axioms: i. Probability of variable A being in state ai (denoted by P(A=ai))5 is a number between 0 and 1. Thus, 4 After Reverend Thomas Bayes (more detail here) 5 As an example, consider the variable A that represents the probability of the car being of a certain color, then the possible states of A are the possible colors of the car. If the po ssible colors (states) are red, blue, green and white, then in order for the states to be mutually exclusive and exhaustive, the car has to have one color and can never have more than one color.

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78 1 ) ( 0 ia A P --2.9 and i ia A P1 ) ( ii. 1 ) ( ia A Pif and only if ai is certain. iii. If A and B are two mutually exclusive events, then the probability that either one or the other will occur is the sum of their individual probabilities, P(A=ai or B=bj) = P(A=aj)+P(B=bi) --2.10 This is known as the additive rule or the theorem on the addition of probabilities. 2.5.3 Law of Total Probability In contrast with the additive rule, joint probability of two events A and B is the probability that both A and B will be in a given state at the same time. Joint probability of independent events is the product of their individual probabilities. Therefore, ) ( ) ( ) (i j i jb B P a A P b B a A P --2.11 Generalizing, probability of n independent events, E1 through En is given by n i i nE P E E P1 1) ( ) ,..., ( -2.12 For example, ( A=aj,B=bi) gives the joint probability of A=aj and B=bi (i.e., the probability of A being in state aj and B in state bi simultaneously). P ( A=aj) and P ( B=bi) are known as the marginal probabilities of aj and bi respectively. One implication of joint probability is the law of total probability The law provides a method to compute the marginal probability of an event (say P ( A=aj)) given the joint probability by summing over all the states of the other variable. Mathematically,

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79 m i i j jb B a A P a A P1) ( ) ( --2.13 where m is the number of possible states of B The operation of summing over all values of bi is also called “ marginalizing over B ”. As an example, assume two fair coins, A and B and consider the question, “What is the probability of getting “heads” on A ?” The question can be an swered by marginalizing over B (i.e., summing over all the states of B in the joint probability of A and B ). The joint probability gives the probability of A and B being in some given state concurrently. Let h represent getting “heads” and t represent “tails”, so in this case, P ( A = h B = h ) represents the joint probabili ty of getting “heads” in A and B simultaneously and P ( A = h B = t ) gives the joint probability of “heads” in A and “tails” in B Adding the two joint probabilities yields P ( A = h ), P ( A = h ) = P ( A = h B = h ) + P ( A = h B = t ) Or i ib B h A P h A P ) ( ) ( where bi are the possible states of B in this case h and t From the above example it is clear that the marginal probability of any variable can be computed by marginalizing (summing over all its states) ov er the variable in the joint probability. This law forms the basis of probabilistic inference. A corollary of this law is that the sum of the joint probabilities over all states of all variables is 1, 1 ) (11 n j m i i jb B a A P -2.14 where n and m are the number of states of A and B respectively.

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80 2.5.4 Conditional Probability Two other concepts of probability calculus that play an important role in BN are conditional probability and conditional independence of variables. This section deals with the first of the two: Conditional probabi lity gives the probability of an event given the probability of another event. P ( A = a | B = b ) = x -2.15 is read as the probability of A = a given the event B = b is x Traditionally, conditional probability is defined in terms of joint probability as ) ( ) ( ) | ( B P B A P B A P -2.16 The following example will be used throughout this section to explain application of relationships to a real pr oblem. The problem statement is to compute the probability of the grass being wet ( W ) given the states of rain ( R ) and cloudiness ( C ). So the probability of rain given cloudiness is ) ( ) ( ) | ( C P C R P C R P -2.17 This example will be referred to as the “wet grass” example in subsequent sections. 2.5.5 Chain Rule According to Pearl (2000), the Bayesian approach to probability deems conditional probability as a more basic relationship between variables than joint probability as it is closer to the organization of human knowledge. Accordingl y, equation (2.13) can be written so as to compute the joint probability in terms of the conditional probabilities ) ( ) | ( ) ( B P B A P B A P -2.18

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81 The above equation denotes the produc t over all the possible states of A and B That is, if A and B are dichotomous variables with states 0 and 1, the joint probability P ( A B ) is given by ) 1 ( ) 0 ( ) 1 | 1 ( ) 0 | 1 ( ) 1 | 0 ( ) 0 | 0 ( ) ( B P B P B A P B A P B A P B A P B A P -2.19 This is known as the chain rule of probability and plays a critical role in BN. Generalizing the chain rule to a set of n events E1, … En, their joint probability is given by the product of the conditional probab ilities of each of the variables. ) ( ) | ( ... ) ,..., | ( ) ,..., (1 1 2 1 2 1 2 1E P E E P E E E E P E E E Pn n n or n j j j nE E E E P E E E P1 1 2 1 2 1) ,..., | ( ) ,..., ( --2.20 The chain rule provides a method to compute the joint probability of all the variables represented in a graphical model (B N). As an illustration, consider a variable representing the state of a sprinkler ( S ) added to the wet grass example of the previous section. The joint probability of all the variables is denoted as ) ( ) | ( ) | ( ) , | ( ) , ( C P C R P C R S P C R S W P C R S W P 2.5.6 Bayes’ Theorem Bayes’ theorem provides method of updating belief in hypothesis B in light of evidence A Elaborating, equation (2. 16) yields the following ) ( ) | ( ) ( ) | ( ) ( A P A B P B P B A P B A P Rearranging these terms leads to the inversion formula which is the heart of Bayesian inference

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82 ) ( ) ( ) | ( ) | ( B P A P A B P B A P -2.21 P ( A | B ) is known as the posterior probability or posterior belief (Bayesian theorists prefer using the term belief values rather than actual probability values to highlight the notion that the values are not traditional probabilistic values ) and is the product of the prior belief ( P ( A )) and the likelihood of B given A ( P ( B | A ) is the likelihood that B will occur given that A is true) divided by a normalizing constant ( P ( B ) can be obtained by marginalizing as in equation (2.11)). The inversion formula (equation 2.19) and the chain rule (equation 2.16) make it possible to compute the conditional probability of any variable in a set of variables if the join t probability over the variables is known. 2.5.7 Conditional Independence One problem with computing the joint probability distri bution is the number of computations required. As equation (2.17) i llustrates, the number of terms required for computing the joint probability increases exponentially with the number of variables; conditional independence offers to redu ce the number terms in many cases. For two variables, A and B if knowing the state of B does not affect the probability of A then A and B are said to be independent of each other; mathematically P ( A | B ) = P ( A ) -2.22 Similarly, P ( A | B C ) = P ( A | C ) implies that A and B are conditionally independent of each other given C ; that is, once C is known, knowing B does not change the belief value of A For example, in the wet grass example, the state of wetness of the grass is conditionally independent of cl oudiness given rain (i.e., give n that it is raining, the probability of cloudiness will not have any effect on the stat e of wetness of the grass).

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83 Generalizing the relationship for a set E of n events { E1, … En}, say there exists a set paj(E) consisting of variables Ej is conditionally dependent upon, such that n j j j nE E E P E E E P P1 1 1 2 1) ,..., | ( ) ,..., ( ) (E (from equation (2.20)) and, )) ( | ( ) ,..., | (1 1Ej j j jpa E P E E E P -2.23 Clearly, if the number of elements in paj(E) is less than n it results in considerable reduction in terms of computation required. 2.5.8 Graphical Notation A brief review of graphical notation and concepts is necessary before further discussion into BN. A graph G ( V,E ) is a function of the set of vertices ( V ) and a set of edges ( E ). Each edge is denoted by a pair of vertices (( A,B ) is an edge connecting the vertices A and B ) and may be directional (denoted by an arrowhead on one end) or unidirectional (also called bi-directional denoted by arrows on both ends or no arrows at all). For bi-direc tional edges, ( A,B ) = ( B,A ) while the same is not true for directional edges, which are denoted by an ordered pair of vertices, the fi rst one denoting the originating vertex for the e dge and the second one denoting the terminating vertex. So ( A,B ) denotes an edge starting at A and ending at B and ( B A ) denotes one from B to A and ( A B ) ( B A ). The vertex of origin is known as the parent of the ending vertex, which is known as the child of the parent. A vertex may have multiple parents or multiple children. Parents of pa rent nodes are known as ancestors ; likewise all vertices descending from any given node are known as its descendants Two vertices with an edge between them are called adjacent vertices. A path in a graph is a sequence of “connected” edges

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84 (the terminating vertex of one edge is the originating vertex for the next, e.g., (( A B ),( B W ),( W E ),( E Z ))). A directed path has all the edges pointing in the same direction. Two edges in a graph are said to be connected if there exists a path between the two edges (in the path listed in the previous example, A and Z are connected), else they are disconnected A path is called a cycle if it begins and ends on the same node (e.g., X Y X distinct from self-loops, e.g., X X ). A graph is cyclic if it contains at least one cycle. The same definition of cycles applie s to both directed and undirected graphs. A directed graph that does not c ontain any cycles is called a directed acyclic graph (DAG). 2.5.9 Causal Networks and d-separation A causal network provides a method for reasoning under uncertainty by constructing a graphical model that represents causal re lationships between events (Jensen, 2001). A directed graph represents the causal relations hips, each elementary variable in the problem forms a node (ver tex) of the network and an edge from A to B can be thought of as “ A causes B ”. This property makes deciding the structure of graphical models more intuitive as compared to other modeling techniques. The d-separation criterion decides how evidence (probability of belief information) is blocked from being transmitted from one node to another (Jensen, 2001) in a causal network. Essentially, there ar e three types of connections in any directed graph; serial diverging and converging as illustrated in Figure 2.10 (a ), (b) and (c) respectively. Intuitively, it is easy to see that information can flow in serial (e.g., A = Cloudy V = Rain B = Wet ) and diverging ( A = hair-length V = Sex B = Stature (Jensen, 2001)) connections unless vertex V is instantiated (has received some ev idence). In situations depicted in Figure 2.10 information can flow from A to B if and only if V is not instantiated.

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85 Specifically, in Figure 2.10 (a), knowing it is raining or not will negate any effect of cloudiness on the state of wetness of grass and in Figure 2.10 (b) knowing the sex of a person nullifies any effect knowledge of statur e may have on hair-length and vice versa. For converging connections however (e.g., A = Rain B = Sprinkler V = Pavement Wet and D = Pavement slippery from Figure 2.10 (c)), information can flow only if the diverging node or any of its descendants is instantiated. For the si tuation in Figure 2.10 (c), information can travel from A to B if and only if V or D is instantiated. (Jensen, 2001). 2.5.10 Bayesian Networks A probabilistic model encodes information that allo ws computing probability of any number of variables ( propositions ) represented in the model connected using Boolean operators. As an example, th e probabilistic model of the variables A, B and C should allow computing the probab ility of all statements like A and B ( A and B ) or ( not C ), and so on. Each such term, formed by connecting the propositions using Boolean operators, is called a well-formed sentence (Pearl, 2000) and is denoted by S. Any joint distribution function (JDF) represents a complete probabilistic model over the variables, since it allo ws computing the probability of any well-formed sentence. The JDF is computed using the additive rule (equation 2.10) and using the following two properties; (a) that every Boolean formula can be represented as a disjunction of elementary events6 (Pearl, 2000), and (b) that elementary events are, by definition, mutually exclusive. Conditional probabilities can be computed in a similar manner using equation (2.16). 6 For example, A and B is the same as not (not A or not B). This is obtained from DeMorgan’s theorem, which states [ NOT( A OR B ) = A AND B ] and [ NOT( A AND B ) = (NOT A ) OR (NOT B )]

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86 By checking if sufficient information is available to compute the probability of every elementary event in the function domain and if the probabilities sum up to 1, the JDF can determine if sufficient information is available to specify a complete probabilistic model and verify whet her or not it is consistent with the data. If the model is inconsistent, it specifies the additional information required and the points at which it is required (Pearl, 2000). From the above discus sion, it should be clear that deriving the correct JDF for a given set of variables al lows computing the probability of any wellformed sentence (i.e., any combination of th e variables). For most practical problems, specifying joint probability functions depends on the problem domain; for continuous variables, they are specified as algebraic expressions (like the normal distribution, exponential distribution, etc.) while various indirect representation methods have been developed for problems involving discrete variables Graphical models are the most promising of such indirect representations (Pearl, 2000). (c) ( a ) e (b) A= Cloudy B= Wet V= Rain A=Hair length A= Rain B=Stature B= Sprinkler V= Sex V= Wet pavement e e e D= Slippery pavement

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87 Figure 2.10 d-separation in (a)serial, (b ) diverging and (c) co nverging connections. Pearl (2000, p. 13) lists three advantages of using graphs in probabilistic and statistical modeling: 1. they provide convenient means of expressing substantive assumptions; 2. they facilitate economical representa tion of joint probability functions; and 3. they facilitate efficient inferences from observations. The second advantage is the most critical; as equation (2.17) illustrates, computing the joint probability of two dichotomous vari ables requires four terms. Extending this, computing the same for n variables requires 2n terms, making the entire calculation very expensive computationally. Clearly, computa tional complexity can be reduced if each term depends only on a small subset of the to tal terms. Graphical models help achieve just such an economy. Graphical models that use undirected graphs are referred to as Markov models (Pearl, 1988) and are used main ly to represent symmetrical spatial relationships (Isham, 1981; Cox & Wermuth, 1996; Lauritzen, 1996). Directed graphical models on the other hand, employ directed graphs and are used to represent causal or temporal relationships (Lauritzen, 1982; Wermuth & Lauritzen, 1983; Kiiveri et al, 1984) and are known as Bayesian networks “[BN are] so named to emphasi ze three aspects: (1) the subjective nature of the input information; (2) the reliance on Bayes’s conditioning as the basis for updating information and; (3) a distinction between causal and evidential modes of reasoning.” (Pearl, 2000, p. 14) More formally, BN are graphical models with the following properties (Jensen, 2001): 1. The graph of the models consists of a set of variables and a set of directed edges between variables. The vari ables form the nodes of the graph and are connected by directed edges. Each variable has a fin ite set of mutually exclusive states.

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88 2. The variables together with the directed edges form a directed acyclic graph (DAG). 3. A conditional probability table (CPT) is attached with each variable. The CPT gives the conditional probability of the variable given its parents. In a BN, conditional independence is implied by the structure of the ne twork. Conditional independence relationships are encoded in th e structure of a BN such that a node is independent of its ancestors given its parents. So for a variable A with parents B1, …, Bn, the CPT is P ( A| B1,…, Bn) and the node is conditionally independent of any parents of Bi. Marginal probability of any variable in a BN can be computed by marginalizing over the joint probability distribution of all the variables in th e network. The conditional independence relationships encoded in the stru cture of the network allow some savings in the number of computations required to com pute the JDF (according to equation 2.23). Two unknowns must be resolved in order to successfully co mpute the JDF and thereby the marginal probabilities, namely the structure of the network a nd the values of the parameters (or conditional probabilities ). Structure refers to the edges of the network and how the various nodes (var iables) are connected to each other. Structure encodes conditional independence relationships between the variables; lack of an edge between A and B denotes A is independent of B7. Specifically, BN encode conditional independence relationships such that a node is independent of its ancestors given its parents. Recall conditional independence from e quation (2.23). In this case, paj(E) is consists of the parents of node Ej. As an example, consider the ne twork shown below (Figure 2.11), the node E6 is independent of E1 and E2 given its parents E3, E4 and E5. The d-separation criterion translates to relationshi ps of conditional independence in BN8. 7 Causality is used in devising the structure of the network and makes it very intuitive. An arrow from A to B can be thought of as A causes B and also represents conditional dependence between the two. 8 The definition of BN does not make any reference to causality and the edges do not necessarily represent causal impact, instead the definition requires for the d-separation properties implied by the network

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89 One point to bear in mind while designing th e structure of a BN is that the aim of the BN is to give cert ainties of events, called hypothesis events that are not directly observable or are observable at a very high co st. These events are grouped into mutually exclusive groups and are called hypothesis variables Variables that are directly observable and provide information rega rding the hypothesis va riables are called information variables Parameters of a BN are conditional probabi lities of each of the variables in the network. Conditional probabilities are represented using a structure known as the Firgure 2.11. Illustration of conditional independence relationships. Conditional Probability Table (CPT), which is essentially a table listing the conditional probabilities for each variable given the rest of the variables in the network. A BN can “learn” the structure from data when the number of variable s used is very large structure to hold (Jensen, 2002). Ho wever, using causality has proved to be a good method of arriving at the structure of the BN (Murphy, 2000). E1E 3 E 4 E 5 E 6 E2

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90 and a substantial amount of data is availabl e. When the structure is known, as in the current study, CPTs are initially specified by an expert (representing the belief of the expert) and are subsequently corrected to ma ke the network conform to real world data. This essentially means that the initial values in the CPTs should be reasonably close or they should at least conform to the same patte rn as the actual values (i.e., one should not specify the probability of rain as 0.0 wh en the probability of cloudiness is 0.96). Determining the correct structure for the networ k and values of the pa rameters is referred to as learning in BN context. The conditional probability relationships between two variables can be thought of as the strength of connection in BN. Once the structure and parameters have been learned, the network can be used for probabilistic inference, that is to infer the state of one variable given a change in the state of others (or to find the states of variables for given uncertain state values for other variables), or to explain away that is, to find the probability of the alterna tive “cause” given the probability of one cause. Using BN for inference is more common of the two. Inference in BN can be exact or approximate which means that the values of variables are computed to conform exactly to the laws of probability or to obtain an approximate value of the same. The first is suited to conditions with a small number of variables with a limited number of states so that computing the values of the variables is not computationally intractable. On the other ha nd, when the number of variables is large, approximate inference is more practi cal. The current study involves only five dichotomous variables, and theref ore implements exact inference. 2.5.11 An Example of a Bayesian Network This section describes the steps involved to build a BN model of the wet grass example. The aim is to develop a model to co mpute the probability of the grass being wet

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91 given the other variables. The first step in building the structure is to identify hypothesis and information variables and determine the relationships between them. This problem has four variables with tw o possible states for each, true (T or 1) and false (F or 0). The variables are cloudy (C), sprinkler (S ), rain (R) and wet grass (W). The network for the problem is depicted in Figure 2.12. Relationships among variables were determined using causal ity: Clouds lead to (cause) rain and not the other way around and they also determine whether the sprink ler is to be turned on or off. Clearly, it would be imprudent to suggest the sprinkler affects the st ate of cloudiness. The figure also shows the CPT for each variable in the network. Conditional pr obabilities can be set by analysis of existing data (e.g., to dete rmine the probability of rain given the probability of clouds from meteor ological data) or they can be subjective belief values set by an expert as explained above. The exam ple and the current study use the latter. Subjective values can be changed so as to make them consistent (according to the rules of probability) with observed data. The JDF must be computed before the model can be used for any predictions. The JDF for the current problem is given by, ) , | ( ) | ( ) | ( ) ( ) , ( R S C W P C R P C S P C P W R S C P --2.24 The above equation can be simplified using conditional independence between cloudiness and wet grass given ra in and sprinkler, that is ) | ( ) | ( ) | ( ) ( ) , ( R S W P C R P C S P C P W R S C P -2.25 For this example, the observed variable is that the grass is wet ( W = 1 ) and the problem is to compute which of the two causes, rain or spri nkler, is the more likely in this case (i.e., to compute and compare the conditional probabilities of rain given wet grass

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92 ( P ( R = 1 | W = 1 )) and sprinkler given wet grass ( P ( S = 1 | W = 1 )) ). According to Bayes’ theorem ) 1 ( ) 1 ( ) 1 | 1 ( ) 1 | 1 ( W P S P S W P W S P --2.26 Note the numerator term in the above equation is the joint probability of W =1 and S =1, that is Figure 2.12 A Sample Bayesian network to de termine model the probability of the grass being wet given states of cloudiness ( C ), Rain ( R ) and Sprinkler ( S ). C S R W P(R=f) P(R=t) C=f 0.8 0.2 C=t 0.2 0.8 P(S=f) P(S=t) C=f 0.5 0.5 C=t 0.9 0.1 S R P(W=f) P(R=t) f f 1.0 0.0 f t 0.1 0.9 t f 0.1 0.9 t t 0.01 0.99 C=f C=t 0.8 0.2

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93 ) 1 1 ( ) 1 ( ) 1 | 1 ( W S P S P S W P Therefore equation (2.26) can be rewritten as ) 1 ( ) 1 1 ( ) 1 | 1 ( W P W S P W S P --2.27 Both the numerator and denominator terms are obtained by marginalizing over appropriate variables in the joint probabil ity distribution of the entire model. So r cW r R S c C P W S P,) 1 , 1 ( ) 1 1 ( --2.28 and, r s cW r R s S c C P W P, ,) 1 , ( ) 1 ( --2.29 In case of the current network, equation 2.28 is expanded as ) 1 1 1 1 ( ) 1 0 1 1 ( ) 1 1 1 0 ( ) 1 0 1 0 ( ) 1 1 ( W R S C P W R S C P W R S C P W R S C P W S P --2.30 The first term in equation 2.30 can be solved according to the JDF equation for the network (equation 2.25), therefore ) 0 1 | 1 ( ) 0 | 0 ( ) 0 | 1 ( ) 0 ( ) 1 0 1 0 ( R S W P C R P C S P C P W R S C P --2.31 All the values required to co mpute the above equation are listed as part of the CPT in Figure 2.12. Plugging the values in the equation, 036 0 ) 9 0 )( 8 0 ( ) 1 0 ( ) 5 0 ( ) 1 0 1 0 ( W R S C P --2.32 Plugging in the values, equation 2.27 yields, 4126 0 6741 0 2781 0 ) 1 ( ) 1 1 ( ) 1 | 1 ( W P W S P W S P --2.33

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94 Similarly the equation for rain given wet grass results 6796 0 6741 0 4581 0 ) 1 ( ) 1 1 ( ) 1 | 1 ( W P W R P W R P --2.34 where the numerator is, 4581 0 ) 1 1 ( W R P --2.35 while the denominator term is the same from equation 2.29, 6741 0 ) 1 ( W P --2.36 Clearly, as seen from the results of e quations 2.33 and 2.34, the sprinkler is the more likely cause of the grass being wet unde r the given conditions. For an illustration of explaining away, consider the probability of the sprinkler being on when it is known that the grass is wet and that it is raining. Knowing grass is we t instantiates the converging connection and allows information to pass thr ough from one variable to another. As a result, knowing grass is wet and that is raining, should result in a decrease in the probability of the sprinkler being on. This is exactly what happens, with 1945 0 ) 1 1 | 1 ( R W S P as opposed to 0.5 when only the state of cloudiness is known. 2.6 Summary Research on attentional bias has been focused at understanding the causes and the underlying mechanisms that drive these biases An overwhelming majority of research has focused on understanding the causes of a ttentional bias, whereas investigating mechanisms has been largely neglected. Va rious cognitive theories emphasize that underlying mechanisms hold at least the same import in understanding attentional biases as their causes (e.g., Williams et al., 1997). Stud y of the mechanisms of attentional bias using paradigms such as the Stroop task a nd the dot probe task is proceeding relative

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95 slowly (compared to advancing of knowledge about the causes), pr imarily because these paradigms offer only an indirect method to study these mechanisms of attentional biases. A direct method of studying these mechanis ms is by developing computer models. Computer simulation of attentional para digm provides an attractive method of investigating underlying mech anisms due to the increase in computational power. Computational power has increas ed roughly by a factor of 10 over the past eight years, which incidentally is the time since the last study involving simulation of an attentional paradigm (i.e., Matthews and Harley (1996 )). Ironically, although it provides a direct measure of attentional bias, th e dot probe paradigm has not been simulated. At the same time, research with the paradigm has ge nerated a very large database and robust relationships between the variables of the ta sk. A computer model can potentially utilize the data and information available about the relationships between variables to possibly provide new insights into the mechanisms of attentional bias from a dot probe perspective. The current study aims to address these i ssues by constructing a NN simulation of the dot probe task. One important objective of the study is also to present BN as a viable and easy to use method of modeling and analyzing data. The study will use established relationships to devise the models and veri fy (or challenge) the models using existing data; leading to questio ns about relationships and opening avenues of new research in the area. CHAPTER 3 METHODS

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96 This chapter presents details regarding th e design, training, and testing of two dot probe models with the Neural and Bayesian network models, respectively. Development and testing specifics will be described for each version of the dot probe that will be simulated, followed by explana tions of the two models. 3.1 The Task The standard version of the dot probe task will be simulated, using pictures as the emotional stimuli (Mogg & Bradley, 1999). The task consists of a pair neutral images, or a neutral image paired with a negative im age, displayed side-by-side for 500 ms. Stimulus offset is followed by appearance of a dot probe stimulus in the spatial location of one of the pictures. Particip ants are instructed to press a button to indicate the side on which the dot appears. The probe remains on the screen for 1100 ms or until the user presses a button to indicate its position. 3.2 Neural Network Model of the Dot Probe task The purpose of the neural network model of the dot probe task will be to compare three different potential causal mechanisms of attentional bias in th e dot probe task. The three mechanisms are: 7. Interaction, based on the model by Williams et al. (1988), which states that attentional bias is a product of the state and trait anxiety levels of an individual and that high anxiety individuals orient towards threatening s timuli and that low anxiety individuals orient away from them. 8. Exposure, based on the premise that all individuals (both high and low anxiety) initially respond in the same manner to both threat and neutral stimuli but that high anxiety individuals are exposed to threat stimuli more th an low anxiety individuals which strengthens the connections for negative stimuli. 9. Intensity. The third one essentially states that attentional bias occurs because high anxiety individuals perceive a stimulus as having a higher thr eat value at that moment than individuals with low levels of trait anxiety.

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97 Two simulations were performed; results for the first are presented in terms of reaction time computed from the number of iterations required to obtain the output. Results for Simulation 2 are presented as activ ation levels of the output units after one iteration. Each mechanism trained the network to be more aroused ( activated ) for negative stimuli as opposed to neutral ones. The mech anisms used the same network, but differed in the training and test pattern s presented, as well as the pa rameters used for training and testing. Results of all three training patterns are compared against the results of the baseline condition. The baseline condition assumed that (1) high and low anxiety individuals respond the same way to all kinds of stimuli, and (2) that both these groups experience a higher level of arousal with for negative stimuli than neutral ones. The details of the mechanisms and the training procedure for each are explained below. According to the initial pr oposal, the network was to be trained for 400 epochs. This requirement was revised to training the network until its mean squared error for that mechanism was less than 0.0001 or the patterns had been presented to the network 500 times (i.e., 500 iterations). Weights were adjust ed online, or at the end of each cycle (that is, after all patterns listed in the table ha ve been presented to the network once). 3.2.1 Mechanisms The network was trained for the negative a nd neutral conditions in isolation. In other words, training input to the network specified the response to a given picture displayed and anxiety level. Training sets for a given mechanism consisted of a fixed number of patterns of each type. The patterns and the frequency with which they were presented to the network are listed in Tabl e 3.1. The mechanism for attention selection,

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98 called the attention mechanism1, was encoded into the network by training the network more at least twice as extensively on patterns re presenting attention to the side of the dot. These patterns are listed in Table3.2. Table 3.1. Training patterns used to train the NN for baselin e, exposure 3x and exposure 5x conditions Table 3.2. Training patterns for the attenti on mechanism for baseline, exposure 3x and exposure 5x conditions. Probe Side (Left/Right) Output (Left/Right) Number of patterns (baseline) Number of Patterns (exposure 3x) Number of Patterns (exposure 5x) Left Left 10 30 50 Right Right 10 30 50 The number of patterns training th e network to attend to the side of the dot was twice the number of patterns training the network to a ttend to the negative image in each condition. 1 This is the mechanism that simulates deliberate human attention towards to attend and respond to the side on which the dot appears. Negative picture side (Left/ Right) Neutral Picture Side (Left/ Right) Trait Anxiety (High/ Low) Output (Left/ Right) Number of patterns (baseline) Number of patterns (exposure 3x) Number of patterns (exposure 5x) Left High Left 5 15 25 Right High Right 5 15 25 Left Low Left 5 5 5 Right Low Right 5 5 5 Left High Left 4 4 4 Right High Right 4 4 4 Left Low Left 4 4 4 Right Low Right 4 4 4

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99 3.2.1.1 Baseline condition The baseline condition was trained usi ng the patterns in Table 3.1. The training assumed that threatening stimuli cause a slightly higher activation than neutral stimuli and so each epoch consists of five patterns presenting a negative stimulus against four patterns for neutral stimuli. 3.2.1.2 Exposure mechanism. The exposure mechanism investigated the possi bility of etiology of attentional bias due to repeated exposure of a high anxiety i ndividual to threat stimuli. Training the network more extensively on certain patterns results in strengthening the connections to produce output consistent with those patterns. Cohen et al. (1990) and Matthews and Harley (1996) used this prope rty of NN to train their networ ks to exhibit a higher degree of automaticity for the word-reading task th an for color naming, presenting 10 times and 8 as many word reading patterns as color nami ng patterns, respectively. As listed in Table 3.1, the current model used the same technique to make the NN more sensitive to negative stimuli for high levels of trait anxiet y and neutral stimuli fo r low levels of trait anxiety. Two exposure mechanisms were simulated, Exposure 3x that trained the network on 3 times as many negative stimuli under hi gh anxiety as the baseline condition, and Exposure 5x that trained the network on 5 times as many negative stimuli as the baseline mechanism. The training patterns for the two mechanisms are listed in Table 3.1. The number of times each pattern was presented to the network is listed in the last column of Table 3.1.

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100 The number of training patterns for the atte ntional mechanism were also increased to offset the increased activation of negativ e stimuli under high anxiety. These training patterns are listed in Table 3.2. 3.2.1.3 Interaction mechanism. The interaction mechanism trained the netw ork to produce results according to the interaction hypothesis, requi ring the network to exhib it the following behavior: 1. Attend toward the negative picture for high levels of trait anxiety and respond faster when the dot repla ces the negative picture. 2. Attend toward from the neutral picture fo r low levels of tra it anxiety and respond faster when the dot repla ces the neutral picture. 3. Produce an output if and only if one of the probe units is activated (to mimic responding to the probe), and the output of the network should be the same as side on which the dot appears. Alternatively, the first two requirement s can be viewed from the reverse perspective as: 1. Attend away the neutral picture for high leve ls of trait anxiety and respond slower when the dot replaces the neutral picture. 2. Attend away from the negative picture for low levels of trait anxiety and respond slower when the dot replaces the negative picture. Training patterns for the interaction mech anism trained the network to specifically attend towards the negative stimulus (and away from the neutral stimulus) under high anxiety and towards the neutral stimulus (and so away from the negative stimulus) under low anxiety. Additionally, the condition assume d that both negative and neutral images resulted in similar activation of the netw ork. This was programmed into the network by presenting the network with an equal number of patterns for negative and neutral stimuli. The training patterns are listed in Table 3.3.

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101 3.2.1.4 Intensity condition The intensity condition was intende d simulate performance under both trait and state anxiety in the NN. The mechanism is ba sed on the assumption that levels of trait and state anxiety regulate the perceived intensity of the stimulus for the individual. Table 3.3. Training patterns used to train the network for the interaction mechanism. Negative picture side (Left/ Right) Neutral Picture Side (Left/ Right) Trait Anxiety (High/ Low) Output (Left/ Right) Number of patterns Left High Left 4 Right High Right 4 Left Low Right 4 Right Low Left 4 Left High Right 4 Right High Left 4 Left Low Left 4 Right Low Right 4 The mechanism essentially was propos ed to be simulated by applying a supernormal input (activation of 8.0 oppos ed 1.0) to the network. Trait anxiety in this condition was to be simulated by applying the supernormal inputs during training while testing with normal inputs. On the other hand, state anxiety was to be simulated by testing the network with supernormal inputs for the negative image applied to the network trained by the baseline mechanism The network could not be successfully trained to simulate trait anxiety but results were obtained for the st ate anxiety condition while two different state anxi ety conditions were tested, us ing an activation value of 4.0 and 8.0 for the negative image under high anxiety respectively.

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102 3.2.2 Simulations Two different simulations were performed for each of the mechanisms; one presented the results in terms of the number of iterations required to compute the output while the other presented them as activations of the output units obtained in one iteration. As one of the simulations listed above simulated the temporal characteristics of the dot probe and presented results in terms of RT, it required changes in computing the net input and output of the network. The following secti ons explain details of the network and further differences in the two simulations. 3.2.3 Structure A two-layer fully connected backpropagati on neural network de picted in Figure 3.1 will be used for all three simulations, in contra st to a partially connected BPN used in the two models of the Stroop task discussed earlier (Cohen et al., 1990; Matthews & Harley, 1994). Input to the network will sp ecify the type of image di splayed on the left and the right, the anxiety level of th e participant and the side on which the dot appears. The model will be built to handle only negative and neutral images. Two units each will be used to specify the characteristics (negative or neutral valence) of the picture on the left ( I1= negative, I2= neutral) and right ( I7= negative, I8= neutral) sides as depicted in Figure 3.1. Two units will specif y the anxiety level ( I4 and I5 for high and low anxiety respectively) of the individual and two units wi ll be used to indicate the side on which the dot probe appears ( I3 and I6 for left and right sides, respectively). The present model will feature one hidden layer of five units, while the output layer will be characterized by two units indicating the possible respons es of “left” and “right”.

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103 Activation of output unit O1 will correspond with the partic ipant pressing the button to indicate the dot appearin g on the left side and O2 will correspond to the right side. 3.2.4 Net Input Simulations 1 and 3 will model the time-cour se of attention and present results in terms of RT. Simulation 2 will compare activation levels obtained in a single iteration and compare activation level and mean square error of the network for the input pattern. Therefore, net input at any step for simula tions 1 and 3 will be a function of the running average of the net input of the preceding time steps, computed using equations 2.5 and 2.6. Net input for simulation 2 will be comput ed using the typical formula presented in equation 2.3. The three e quations are listed below.2 ) 1 ( ) 1 ( ) ( ) ( t x t x t xj j j --2.5 where i ij i jb w t a t x ) ( ) ( --2.6 b w a xi n ij i j --2.3 A normally distributed random bias will be added to the net input in all three simulations to mimic variability of performance, reminiscent of the Cohen model (Cohen et al., 1990). 3.2.5 Activation Activation for the hidden and output units will be computed by applying the logistic sigmoid function of equation 2.3 to th e net input computed in the previous step. 2 The numbers of the equations are the same as used in Chapter 2.

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104 Figure 3.1 Neural network model for simulating dot probe task. 3.2.6 Output For all simulations, activation level of th e unit will form the output of each hidden unit. Output of the output units (and therefor e the network )will be computed on the basis of a random walk or diffusion process by addi ng a small amount of evidence according to equation 2.8 to each unit on each iteration. A threshold value of 1.0 will be set for these units such that they will be considered to be active only when the evidence of the unit exceeds 0.1. No threshold will be set for output of simulation 2 and the activation level of each unit will be considered as its output. RIGHT IMAGE H5 O1O2 H1 H4H2H3I1 I2I3I4I5I6 I7 I8 Input Units Hidden Units Output Units 2n d Weight Layer ( w2) 1s t Weight Layer ( w2) LEFT IMAGE ANXIETY Ne g ati v e Neutra l Hi g h Low PROBE LEFT PROBE RIGHT Ne g ative Neutra l LEFT RIGHT

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105 3.2.7 Initialization Initialization of the networ k for all three simulations will involve assigning random weights between 0.0 and 1.0 to the connections in the network. These weights will be adjusted to yield the correct output fo r given input during the training phase. 3.2.8 Training Training patterns for each of the simulati ons have already been explained in the previous section (Simulations). 3.2.9 Testing The network will simulate presenting images to 10 high anxiety and 10 low anxiety individuals. Each participant will be pr esented with five trials of each possible combination of stimuli (Table 3.1). Results fo r Simulation 1 are presented in terms of RT computed by deriving relationships between th e number of iterations required to compute the output and the typical output for the condi tion while the activati on of the output units are compared for Simulation 2. 3.3 Bayesian Network The first task in constructing the BN model of the dot probe task is to identify the hypothesis and information variables. Recall that hypothesis variables are the ones that either are not observable or observa ble only at a very high cost and information variables provide information about the hypothesis variables. The hypothesis and information variables to be modeled in the BN are chos en from among the independent and dependent variables of the dot probe task3 to be modeled. The primary independent variables are: 4. The valence and arousal level of the picture. 5. Participant’s level of trait anxiety 3 The same version of the dot probe will be mode led by the BN as will be simulated by the NN.

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106 6. The side on which the probe appears. And the dependent variables are 1. The direction of attention. 7. The RT in responding to the probe. RT constitute s the fifth variable in the BN. Independent variables are by definition, obs ervable and therefore classified as information variables. Of the two dependent va riables, RT is also an observed variable and so is classified as an information variab le. That leaves only the direction of attention as the hypothesis variable. As direction of a ttention is precisely what the dot probe (and other attentional paradigms) are used to infer, the BN provides an ideal modeling framework. To model a variable in a BN, it must be di screte and have a finite number of states. The BN representing a model of the five va riables of the dot pr obe task is shown in Figure 3.1. The number of states, their name s, their possible values and the meaning of each variable in a Bayesian and real world context are explained below. 8. Arousal Rating (AR): As variables should be discrete and have a finite number of states, this node of the BN will represent the arousal rating of the image. The “probability” of the variab le was the normalized arousal rating of th e displayed image, thereby making the model independent of the rating tool used. Thus, it is possible to represent either the IAPS rati ng of the picture or its SAM rating. The current study used the former. Indeed the ne twork could also prove to be a tool to check how closely one rating matches the ot her. Valence of th e picture will not represented in the model, so it is assu med the arousal rating represents negative image. Further, the neutral image in a cri tical trial is assumed to have an arousal rating of 0.0 and so is ignored in the model. The variable had two possible st ates, negative = true (1.0) and negative = false (0.0) (or neutral= true). A value of 1.0 de noted an image with the highest possible negative rating (the specific highest value will depend on the arousal scale used). A value of 0.75 means that the image is ne gative with probability 0.75 for the model and the image has an arousal rating of 0.75 on the arousal scale in the dot probe context. 9. Anxiety (Anx): This node denoted the level of tr ait anxiety of an individual. The variable also had two possible states, high= true (1.0) and high=false (0.0) (or low= true ). The variable represented the pr obability of the individual having high level of trait anxiety computed by normaliz ing the anxiety score of the individual

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107 on an anxiety questionnaire. Different anxi ety questionnaires could have been used to obtain the trait anxiety score but the cu rrent study will relied on the STAI-Trait. 10. Attention Direction (AD): This was the sole hypothesis variable (variable not directly observable) in the current Baye sian model; it is directly influenced by AR and Anx According to the cognitive mode l proposed by Williams et al. (1988), perception of the valence and arousal level of the stimulus coupl ed with level of trait anxiety decide the di rection in which an individual will orient attention. Following the same line of reasoning, attenti on direction can also be interpreted as a measure of the strength of attentional bias States of the vari able reflect whether attention direction is towards or away from the negative image, as towards = true (1.0) and towards = false (0.0) (or away = true ) from the negative image. Note that the connection between AR Anx and AD is a converging connection. By the rules of d-separation, this means that information cannot travel from AR to Anx and vice-versa if either AD or at least one of its des cendants is instantiated (i.e., their state is known). For in stance, if it is known that an individual is attending towards ( towards = true ) the negative image, information about anxiety ( Anx ) will not add to knowledge about the arousal level of the picture ( AR ). 11. Probe Side (PS): This variable simply denoted th e side on which the dot appeared. Like AD its possible states are either on the side of the negative picture ( PS = Neg [1.0]) or on the opposite side as the negative picture ( PS= Ntrl [0.0]). Unlike the other variables, values between 0.0 and 1.0 we re not allowed to represent its states. 12. Reaction Time (RT): For this model, RT was assumed to have only two states, high and low. The two are denoted as RT= low (1.0) and RT= high (0.0). One of the issues the model was intended to was the existence of a linear relationship between the probability of obtaini ng a high RT and the actual RT. CPT for each variable are not listed in the figure. The CPT table for a variable indicates the probability of the variable being in one of the state given its parents. The crucial CPT required was that of P ( AD | AR Anx ), that is, the conditional probability of AD given the probability of AR and Anx These values were computed from a study conducted at the Motor Behavior Laboratory at the University of Florida as follows: 13. Outliers were eliminated (RT of < 200 ms and >1000 ms). 14. If the RT was greater one standard devi ation (positive) of the mean, attention direction was assumed to be on the side of opposite of probe-side, else it was assumed to be on the side of the probe. Average of individuals attending towards and away from the negative picture was computed to form the CPT.

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108 Attention was assumed directed towards the negative image when RT was low for a probe replacing the negative image and high for an image replacing the neutral image. RT was said to be low if it was one SD devi ation less than the mean and was said to be fast if it was more than one SD more than the mean. Average of these numbers were com Figure 3.2 Bayesian network m odel of the dot probe task. After establishing the CPTs for each of the variables, the model will was used to attempt to answer the following questions: 10. What are the probabilistic relationships be tween the variables? Specifically, the model was used to obtain the probability of an individual attending to the negative image given the anxiety level of the indivi dual and the arousal ra ting of the picture displayed. In order to do this, AD was set to 1 (Negative = 1, i.e., participant is attending towards the negative cue with probability 1.0), and the AR was obtained for different levels of anxiety. This eff ectively yielded the arousal level for the given probability, required so that the individual attends to the negative cue with probability 1. Similarly, the relationship was investigated by recording the change in the value of anxiety due to changes in the arousal rating. Arousal (Neg./Neutral) Anxiety (High/Low) Attn Dir (Neg/Ntrl.) Probe Side (Neg./Ntrl.) Reaction Time (High/Low)

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109 11. Is there a specific anxiety score that can be used as a threshold to high anxiety? This was ascertained from the pattern of change in the arousal level given the anxiety score. 12. What is the accuracy of the model? Dete rmined by checking the results obtained from the model against re sults of the actual study.

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110 CHAPTER 4 RESULTS 4.1 Neural Network Model The neural network model was trained on three different conditions, namely the basic exposure, and interaction, until either the network ach ieved a mean squared error below a preset value (0.0001) or exceeded a predetermined arbitrar y number of iterations (500). The number of iterations that the netw ork took to train for each of the conditions, and the final error after trai ning, is listed in Table 4.1. Two different sets of test patterns were used for the neural network (NN) model; a basic model, that only specified whether a gi ven unit was activated or not, and a set of patterns specifically to test for the intensity condition. Te st patterns for the intensity mechanism had elevated levels of activation for negative stimuli to simulate a higher perceived arousal level of the negative stimul us. As a result, anxiety for the intensity condition refers to state anxiety while for all the other test cases it refers to trait anxiety Basic test patterns are presente d in Table 4.2 and the intensity test patterns are listed in Table 4.3. Table 4.1. Number of training iterations and MSE for each training mechanism. Condition Number of training iterations Mean Squared Error Baseline 18 0.000049 Exposure 3x 24 0.000096 Exposure 5x 18 0.000060 Interaction 500 0.000956 Each column of Table 4.2 and Table 4.3 repr esents the activati on presented to an input unit of the network. The first two colu mns represent information about the picture

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111 appearing on the left side and the last two columns represent information about the picture on the right side. So, a negative pict ure appearing on the left is represented by setting the first input unit to 1.0. Similarly, th e side on which the dot appears is indicated by the appropriate probe unit. Denoted by a “1” if activated, anxiety of the individual is encoded by activating the high or low anxiety units also de signated by a “1” if active. The numbers in parentheses denote th e index-number of each input unit. Patterns 1 through 4 represent the possible combinations for high anxiety ; patterns 1 and 2 represent the match condition that is, when the dot follows th e negative picture. Specifically, pattern 1 represents match-left and pattern 2 represents match-right ( left and right refer to the side of the dot ). Patterns 3 and 4 denote the mismatch conditions, that is, conditions in which the dot replaces the neutral im age. Specifically pattern 3 is called mismatchright (because the dot probe appears on th e right) and pattern 4 is called mismatch-left (because the dot probe appears on the left). Patterns 5 through 8 encode the same information for a low anxiety individual and so differ from the first four patterns onl y in the activation of the anxiety unit. Consequently, the numbers 1 through 4 are us ed to refer to patte rns 5 through 8 along with stating the anxiety level specificall y. All results refer to these patterns. The intensity mechanism presented in Table 4.3, diffe rs from the other conditions in an elevated level of activation of the nega tive stimulus is designated for high levels of state anxiety Therefore, patterns 5 through 8 remain unchanged from the basic patterns and are not listed, while the activation le vel for the negative picture in patterns 1 through 4 is increased to 4.0.

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112 The weights and biases for the network af ter training for the basic, exposure and interaction conditions are lis ted in the Appendix. Although it was initially proposed that training for the exposure condition would ‘expose’ the network to three times as many Table 4.2. Basic test patterns for the neural network model Pattern Number Left Pic. Negative (1) Left Pic Neutral (2) Left Probe (3) High Anxiety (4) Low Anxiety (5) Right Probe (6) Right Pic. Negative (7) Right Pic. Neutral (8) 1 match left 1 0 1 1 0 0 0 1 2 match right 0 1 0 1 0 1 1 0 3 mismatch right 1 0 0 1 0 1 0 1 4 mismatch left 0 1 1 1 0 0 1 0 5 match left 1 0 1 0 1 0 0 1 6 match right 0 1 0 0 1 1 1 0 7 mismatch right 1 0 0 0 1 1 0 1 8 mismatch left 0 1 1 0 1 0 1 0 Table 4.3. Test patterns for the intensity condition. Pattern Number Left Pic. Negative (1) Left Pic Neutral (2) Left Probe (3) High Anxiety (4) Low Anxiety (5) Right Probe (6) Right Pic. Negative (7) Right Pic. Neutral (8) 1 4 0 1 1 0 0 0 1 2 0 1 0 1 0 1 4 0 3 4 0 0 1 0 1 0 1 4 0 1 1 1 0 0 4 0 negative patterns as the basic conditi on, another exposure condition was added to test the effect of further exposure to a hi gh anxiety individual. The condition simulated

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113 presenting a high anxiety indivi dual with five times as ma ny negative stimuli. Final weights and biases for this condition are also presented in the Appendix. 4.1.1 Results for Simulation 1: RT. The intent of this simulation was to presen t results for all thr ee conditions in terms the response time (RT), computed by deri ving equations to conve rt the number of iterations required to co mpute the output (RT) for that condition. A robust set of such equations (to convert number of response iter ations to RT) could not be established and so results for this simulation are presented in terms of the number of iterations required to compute the output. Table 4.4 lists the results for all conditions with high levels of trait anxiety while Table 4.5 lists the same for low levels of trait anxiety The interpretation of the anxiety condition (i.e., whether it is trait or state anxiety), depends on the condition being simulated. Specifically, the intensity condition simulates performance on the dot probe task under high levels of state anxiety while the other two conditions, exposure and interaction simulate performance under high levels of trait anxiety. The first column in each table lists the name of the condition. The dot probe task requires participants to indicate the side on which the dot appeared. The same was also required of the model; that is, to have the model output the side on which the dot appeared. The interact ion and both intensity mechanisms could not produce the correct output for mismatch patterns. Baseline mechanism. In this training mechanism, the network was exposed to five negative stimuli and four neutral ones in each epoch for both high and low anxiety. The condition assumed similar reaction to both ne gative and neutral stimuli under both high and low anxiety conditions, thus simulating the response of a part icipant with normal

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114 level of anxiety. As expected, the network re sponded with the correct output for all input patterns, that is, it correctly followed the side on which the dot appeared. An unexpected result was that under high anxiety the network responded faster when the negative Table 4.4. Results of Simulation 1 under conditions of high anxiety. Condition Number of Iterations EvidenceLeft Output Unit EvidenceRight Output Unit Pattern 1: AnxietyHigh, Negative Pic. Left, Probe Left. Correct Output Left ( Match Left ) Basic 8 1.00412 -0.83204 Exposure 3x 8 1.00486 -0.83278 Exposure 5x 8 1.00487 -0.83279 Interaction 8 1.00476 -0.83268 Intensity 8 1.0047 -0.83262 Intensity 8 8 1.00472 -0.83264 Pattern 2: AnxietyHigh, Negative Pic. Right, Probe Right. Correct Output : Right ( Match Right ) Basic 10 -0.69662 1.09567 Exposure 3x 9 -0.84056 1.07813 Exposure 5x 9 -0.8562 1.09377 Interaction 10 -0.67263 1.07168 Intensity 9 -0.84577 1.08334 Intensity 8 9 -0.85023 1.0878 Pattern 3: AnxietyHigh, Negative Pic. Left, Probe Right. Correct Output : Right ( Mismatch Right ) Basic 9 -0.8549 1.09246 Exposure 3x 9 -0.85619 1.09375 Exposure 5x 9 -0.8562 1.09376 Interaction 11 1.09849 -0.70685 Intensity 10 1.14387 -0.74483 Intensity 8 8 1.00243 -0.83035 Pattern 4: AnxietyHigh, Negative Pic. Right, Probe Left. Correct Output : Left ( Mismatch Left ) Basic 10 1.13939 -0.74035 Exposure 3x 11 1.11164 -0.72 Exposure 5x 8 1.00476 -0.83268 Interaction 10 -0.60555 1.00459 Intensity 9 -0.79285 1.03041 Intensity_8 10 -0.63408 1.03313 picture appeared on the left than when it appeared on the right. The network took 8 iterations to compute the output under the match condition when the negative picture was on the left as opposed to 10 when the picture appeared on the right Similarly, it took 9

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115 iterations for the mismatch right (probe on right but negative image left) condition versus 10 on the mismatch right. A similar pattern of fa ster response to negative picture was not Table 4.5. Results of Simulation 1 under condition of low anxiety. Condition Number of Iterations Evidence Left Output Unit Evidence Right Output Unit Pattern 1: AnxietyLow, Negative Pic. Left, Probe Left. Correct Output Left ( Match Left ) Basic 10 1.1538 -0.75475 Exposure 3x 10 1.07328 -0.67424 Exposure 5x 8 1.00486 -0.83279 Interaction 10 1.14758 -0.74853 Intensity 10 1.14923 -0.75018 Intensity 8 10 1.14979 -0.75075 Pattern 2: AnxietyLow, Negative Pic. Right, Probe Right. Correct Output : Right ( Match Right ) Basic 10 -0.663 1.06205 Exposure 3x 9 -0.83967 1.07724 Exposure 5x 9 -0.8562 1.09377 Interaction 9 -0.77923 1.01679 Intensity 10 -0.67575 1.0748 Intensity 8 10 -0.66966 1.0687 Pattern 3: AnxietyLow, Negative Pic. Left, Probe Right. Correct Output : Right ( Mismatch Right ) Basic 9 -0.85449 1.09205 Exposure 3x 9 -0.85618 1.09375 Exposure 5x 9 -0.85617 1.09374 Interaction 9 -0.83441 1.07198 Intensity 9 -0.85485 1.09242 Intensity 8 9 -0.85467 1.09224 Pattern 4: AnxietyLow, Negative Pic. Right, Probe Left. Correct Output : Left ( Mismatch Left ) Basic 10 1.14272 -0.74367 Exposure 3x 10 1.04377 -0.64473 Exposure 5x 8 1.00457 -0.83249 Interaction 11 1.10457 -0.71292 Intensity 10 1.14661 -0.74757 Intensity 8 10 1.14914 -0.75009 that apparent for low anxiety. Results of the baseline mechanism provided a yardstick by which the results of the other conditions c ould be measured and thereby

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116 allow measurement of the efficacy of the training mechanism in producing the desired results. Exposure. Training the exposure condition took longer than the baseline condition (24 cycles versus 18). The mechanism consisted of exposing the network to three times as many patterns of negative stimuli as the baseline mechanism under high anxiety for each epoch. The resulting network produced the output faster than the baseline mechanism in the match right (9 iterations against 10) and slower in the mismatch right (11 iterations against 10) condi tions. The trend of reacting to negative pictures appearing on the left persisted in this condition as well, although the difference was reduced in the match condition and increased in the mismatch conditions. To determine if repeated exposure to the same stimuli had any further effect on the performance of the network, the network wa s trained on five times as many negative stimuli under high anxiety as in the baseline mechanism. Results of this are listed as “Exposure 5x”. To avoid confusion, the basic exposure mechanism will be referred to as “Exposure 3x” throughout the remainder of this text. As can be seen, performance mostly remained the same as the Exposure 3x mechanism except for an observed speed up in case of mismatch left. Both the exposure conditions displayed the existence of an attentional bias by responding faster for the match conditi ons as opposed to mismatch conditions when the negative pictur e appeared on the same side. Performance of the network for the Exposure 3x mechanism for low anxiety (Table 4.5) remained virtually unchanged from th e baseline condition except for a slight decrease observed in the number of response iterations for match-right condition (9 iterations as opposed to 10). On the other ha nd, continued exposure, as represented by the

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117 Exposure 5x mechanism, resulted in quicker response times for low anxiety in three of the four trials (namely, match-left, match-ri ght and mismatch-left) as compared to the baseline mechanism, and in half the trials (match-left and mismatch-left), when compared with the Exposure 3x mechanism. Implications of this result are discussed in Chapter 5. Further, the trend of responding to salient stimuli appearing on the left was largely absent in this case. Interaction. Although the interaction mechanism correctly simulated response to all test patterns for low anxiety and the ma tch conditions for high anxiety, the mechanism completely failed to output the correct re sponse in both mismatch conditions for high anxiety. The trend of favoring ne gative pictures appearing on th e left side continued with the current mechanism also. The mechanism gives some insight into the inappropriateness of the inte raction hypothesis as repr esented in this network. Intensity. Two intensity mechanisms were simu lated, each one presenting the input unit for the negative unit with a higher activation under high anxiety as opposed to low anxiety. Both the mechanisms used the netw ork trained in the baseline condition. The basic intensity mechanism presented an activ ation value of 4.0 while the second intensity mechanism ( Intensity 8 ) doubled the activation value to 8.0. The mechanism reduced the response times in the match conditions from the corresponding times under the baseline mechanism but, like the inte raction mechanism, could not produce the correct output for both the mismatch conditions under high anxiety 4.1.2 Results for Simulation 2: Activation. Simulation 2 involved computing the final results obtained by running the network for one iteration only. Table 4.6 lists the result s for this simulation for high and low

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118 Table 4.6. Simulation 2: Output activ ations for high and low anxiety. Condition Activation Left Output Unit Activation Right Output Unit Pattern 1: Negative Pic. Left, Probe Left. Correct Output Left ( Match Left ) High Anxiety Low Anxiety Left Right Left Right Basic 0.999906 0.000149 0.999904 0.000118 Exposure 0.999996 0.000000 0.999995 0.000000 Exposure 5x 0.999911 0.000105 0.999932 0.000082 Interaction 0.999968 0.000024 0.999910 0.000064 Intensity 0.999980 0.000022 0.999934 0.000079 Intensity 8 0.999978 0.000044 0.999203 0.001738 Pattern 2: Negative Pic. Right, Probe Right. Correct Output Right ( Match Right ) High Anxiety Low Anxiety Left Right Left Right Basic 0.000686 0.999647 0.000429 0.999627 Exposure 0.000000 0.999983 0.000000 0.999989 Exposure 5x 0.000500 0.999654 0.000379 0.999809 Interaction 0.000062 0.999965 0.000883 0.999528 Intensity 0.000056 0.999962 0.000404 0.999794 Intensity 8 0.015610 0.988949 0.022888 0.975376 Pattern 3: Negative Pic. Left, Probe Right. Correct Output : Right ( Mismatch Right ) High Anxiety Low Anxiety Left Right Left Right Basic 0.002218 0.999012 0.000550 0.999775 Exposure 2.76E-10 0.999991 0.000000 0.999984 Exposure 5x 0.001175 0.999576 0.002603 0.998420 Interaction 0.999982 0.000022 0.002141 0.999316 Intensity 0.999979 0.000032 0.002796 0.998291 Intensity 8 0.999951 0.000079 0.017336 0.987412 Pattern 4: Negative Pic. Right, Probe Left. Correct Output : Left ( Mismatch Left ) Low Anxiety Left Right Left Right Basic 0.999713 0.000483 0.999867 0.000131 Exposure 0.999619 8.80E-08 0.99919 0.000000 Exposure_5x 0.999884 0.000181 0.999815 0.000125 Interaction 0.000186 0.999953 0.999809 0.000213 Intensity 0.000152 0.999942 0.999821 0.000120 Intensity_8 0.094360 0.955398 0.999974 0.000071 anxiety individuals. Although activations of output units do not apply to the dot probe as clearly and directly as the number of iterations to com pute the response times, such values are more robust than the number of response iterations as fewer variables are

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119 required to be in agreement to replicate the results. More important ly, activation data is indispensable in verifying the accuracy of a NN model. The activation values are consistent with the results of Simulation 1. One finding emerging from the activation values is that when the activation value is increased (as in the intensity-8 mechanism) the activation of th e correct output unit decreases while the activation of the incorr ect unit increases. Th is points towards an increase in error in the dot probe performance under high state anxiety. 4.2 Bayesian Network Model One of the most crucial aspects of proba bilistic modeling using Bayesian networks (BN), at par with establishing the struct ure of the network, is determining the conditional probability tables (CPTs). The CPTs for each variable were computed according to the method outlined in Chapter 3, and are shown in Table 4.7. Arousal rate ( AR ), anxiety (Anx) and probe side (PS) are independent variables. Values in the CPTs list the prior probabilities of each of these variables. Ta ble 4.7 (a) lists the prior probability for AR; the values of 0.5 for negative arousal rate indicates a mild ly arousing negative picture. Similarly, in Table 4.7 (b), prior probability of 0.5 speci fies that a given individual is equally likely to have high and lo w levels of trait anxiety. The fact that for any trial, the dot probe is equa lly likely to appear replacing th e negative image as it is for the neutral image is highlighted w ith prior probabili ty values of 0.5. The critical CPT is that of the variable attention direction (AD). The variable

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120 Table 4.7. Conditional Probability Tables for variables Arousal Rating (AR ), Anxiety ( Anx ), Probe Side ( PS ), and Reaction Time ( RT ) depends upon the anxiety and arousal level of the negative image. CPTs for this variable were established using the procedure outlined in Chapter 3. Three different CPTs wereset up, (a) using the data of all the conditions, (b) using data when the negative image appeared on the left only, and (c) by using data from trials in which the negative picture appeared on the right. Values for th ese conditions are shown in Table 4.8. After establishing the CPTs, the network was used to compute the posterior probabilities of AD=negative AR=negative and Anx=high Following the initial computation of prior probabil ities, the effect of knowing Anx= high in addition to Table 4.8. Conditional Probability Tables for variable AR for the Bayesian network. Case 1: All data Ca se 2: Data from left only Case 3: Data from right only AR= Neg Anx = High AD= Neg AD= Ntrl AD= Neg AD= Ntrl AD= Neg AD= Ntrl 0 0 0.5 0.5 0.5 0.5 0.5 0.5 0 1 0.5 0.5 0.5 0.5 0.5 0.5 1 0 0.5035 0.4965 0.5416 0.4583 0.4638 0.5362 1 1 0.5068 0.4932 0.5211 0.4789 0.4933 0.5067 AR= Neg AR= Ntrl 0.5 0.5 (a) Anx=High Anx= Low 0.5 0.5 (b) PS = Neg PS = Ntrl 0.5 0.5 (c) AD=Neg PS=Neg RT=Low RT=High 0 0 0.95 0.05 0 1 0.05 0.95 1 0 0.05 0.95 1 1 0.95 0.05 (d)

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121 PS=Neg and RT = Low on the posterior probabilities of AD and AR was computed. The same effect for knowing the state of AR on the probabilities of AD and Anx was also computed. These posterior probabilities are listed in Table 4.9, Table 4.10, and Table 4.11, respectively. The first row of each table yields the posterior probabilities of AR=negative (i.e., the image is negative), AD= negative (i.e., the individual attends towards the negative image) and Anx=high (i.e., the probability th at anxiety level of th e individual is high) given that the probe replaces the negative image ( PS = Neg ) and the recorded RT is low ( RT=low ). A comparison of the three tables hi ghlights the import of accuracy of the CPTs. This is discussed further in Chapter 5. Table 4.9 Posterior probabilitie s of various variables com puted given the evidence (in bold) using the CPT derived from all data. AR= Neg AD=Neg Anx=high PS=Neg RT=low Prior Post Prior Post Prior Post Evidence Evidence 0.5 0.5023 0.5026 0.9505 0.5 0.5007 1 1 0.5 0.4977 0.5026 0.0505 0.5 0.4993 0 1 0.5 0.503 0.5026 0.9506 1 NA 1 1 0.5 0.4969 0.5026 0.0506 1 NA 0 1 0.5 0.5016 0.5026 0.9503 0 NA 1 1 0.5 0.4984 0.5026 0.0503 0 NA 0 1 1 NA 0.5026 0.951 0.5015 1 1 1 NA 0.5026 0.051 0.4985 0 1 Table 4.10 Posterior probabilities of various variables computed gi ven the evidence (in bold) using the CPT derived from data using pictures appearing on the left only. AR= Neg AD=Neg Anx=high PS=Neg RT=low Prior Post Prior Post Prior Post Evidence Evidence 0.5 0.5137 0.5157 0.9529 0.5 0.4955 1 1 0.5 0.4855 0.5157 0.0531 0.5 0.5047 0 1 0.5 0.5093 0.5157 0.952 1 NA 1 1 0.5 0.4903 0.5157 0.052 1 NA 0 1 0.5 0.4806 0.5157 0.541 0 NA 1 1 0.5 0.518 0.5157 0.9538 0 NA 0 1 1 NA 0.5157 0.9556 0.5 0.4913 1 1 1 NA 0.5157 0.0563 0.5 0.5098 0 1

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122 Table 4.11 Posterior probabilities of various variables computed gi ven the evidence (in bold) using the CPT derived from data using pictures appearing on the left only. AR= Neg AD=Neg Anx=high PS=Neg RT=low Prior Post Prior Post Prior Post Evidence Evidence 0.5 0.4902 0.4893 0.9479 0.5 0.5068 1 1 0.5 0.5095 0.4893 0.048 0.5 0.4935 0 1 0.5 0.497 0.4893 0.9494 1 NA 1 1 0.5 0.503 0.4893 0.0494 1 NA 0 1 0.5 0.4832 0.4893 0.9464 0 NA 1 1 0.5 0.5158 0.4893 0.0467 0 NA 0 1 1 NA 0.4893 0.9458 0.5 0.5138 1 1 1 NA 0.4893 0.0461 0.5 0.4872 0 1 The BN model was also used to test the eff ect of a change in trait anxiety levels on the posterior probability of both AR and Anx given that the indivi dual is known to be attending towards the negative image. These co mputations were carried out only with the CPT obtained by considering all trials from th e available data and are presented in Table 4.12 through Table 4.15. Although the model perfo rmed the computations, interpretation of the results obtained is not straightforward and is riddled with ambiguities. These are highlighted in Chapter 5, along with an e xplanation and discussion of the results. Table 4.12 Prior and posterior probabilities for various prior probability values of AR= Neg. AR= Neg AD=Neg Anx=high PS=Neg RT=low Prior Post Prior Post Prior Post Evidence Evidence 0.25 0.2427 0.5026 0.949 0.5 0.5034 1 1 0.5 0.4902 0.5026 0.9479 0.5 0.5068 1 1 0.75 0.7425 0.5026 0.9469 0.5 0.5103 1 1 1 1 0.5026 0.9458 0.5 0.5138 1 1 Table 4.13 Prior and posterior probabilities for various prior probability values of Anx= high AR= Neg AD=Neg Anx=high PS=Neg RT=low Prior Post Prior Post Prior Post Evidence Evidence 0.5 0.4832 0.4856 0.9464 0 0 1 1 0.5 0.4867 0.4856 0.9472 0.25 0.2551 1 1 0.5 0.4902 0.4856 0.9479 0.5 0.5068 1 1 0.5 0.4936 0.4856 0.9486 0.75 0.755 1 1 0.5 0.497 0.4856 0.9494 1 1 1 1

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123 Table 4.14 Prior and post erior probabilities of Anx= high for various prior probability values of AR= Neg given AD= neg. AR= Neg AD=Neg Anx=high PS=Neg RT=low Prior Post Prior Post Prior Post Evidence Evidence 0.25 0.2419 1 NA 0.5 0.5037 1 1 0.5 0.489 1 NA 0.5 0.5075 1 1 0.75 0.7417 1 NA 0.5 0.5114 1 1 1 1 1 NA 0.5 0.5154 1 1 Table 4.15 Prior and post erior probabilities of AR= Neg for various prior probability values of Anx=high given AD= neg. AR= Neg AD=Neg Anx=high PS=Neg RT=low Prior Post Prior Post Prior Post Evidence Evidence 0.5 0.4812 1 NA 0 0 1 1 0.5 0.4852 1 NA 0.25 0.2557 1 1 0.5 0.489 1 NA 0.5 0.5075 1 1 0.5 0.4929 1 NA 0.75 0.7556 1 1 0.5 0.4966 1 NA 1 1 1 1

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124 CHAPTER 5 DISCUSSION The purpose of the current study was two-fo ld; (1) to simulate performance on the dot probe task under high and low levels of a nxiety using a neural network (NN) and (2) to provide a new method of analyzing the resu lts of the dot probe a nd allow emergence of probabilistic relationships among variables using a Bayesian network (BN) model. Results of various simulations are interpre ted and discussed below; a rationale is provided for the findings and future research directions are proposed. 5.1 Neural Network Model The basic aim of the NN model was to te st three potential mechanisms explaining attentional bias as understood from the fi ndings of the dot probe and to provide a common ground to compare results obtained fr om the three. The study also represented the first known attempt to simulate performa nce on the dot probe using a NN. Despite our lofty expectations, the model fell short of providing an accurate simulation of human performance on the dot probe task. However, the model was able to simulate the basic empirical findings of the dot probe. Although fina l results could not be depicted in terms of response time (RT), as was the original in tent of the study, RT differences could still be estimated using the number of iterations required to compute the output for each mechanism. Various aspects of the NN and th e explanations to the failure of the model are discussed below.

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125 5.1.1 Weights of the Network. Appendix A lists the weights of the NN af ter training for each of the mechanisms. The network was initialized by randomly a ssigning weights between 0 and 1 to all connections and biases. Training for each mech anism started from the same initial state and ended when the mean squared error (M SE) was within tolerance (<0.0001) or the network completed 500 epochs, whichever was earlier. For all training mechanisms, except the interaction mechanism, the netw ork managed to achieve MSE within the specified limits. Cohen et al. (1997) explaine d Stroop effects on the basis strength of processing (SOP) which refers to higher activation levels of the some of the units of the network either due to strengthened connections betw een the units or due to a higher resting activation of the unit. However, the concep t is not directly applicable for every mechanism employed in the current study because the NN lacks the pathways that were a basic element of the Cohen model.1 So even though the some units have higher activation levels due to increased strength of connectio ns, interpreting the increased activation for the dot probe is not straightforward. An in teresting observation is that the connection weights for Exposure 5x are not necessarily greater in magnitude than the Exposure 3x mechanism, leading to the conc lusion that repeated exposure to a subset of the patterns does not increase the connecti on strength of all the connect ions but increases the net effect of the stimuli related to those patterns. In other words, the same activation pattern results in a higher activation at the output level even though no t all the weights related to that pattern are strengthened. Th is can also be viewed as an increase in efficiency of the 1 Recall that the Cohen model was a partially connected NN, with connections forming separate pathways for each of the two tasks, color naming and word reading. See Chapter 2 for details.

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126 network, where weights are adjusted to handle the specific tr aining patterns more efficiently. Weights can also be used to explain the small range of the number of iterations required to compute the output (which led to a failure of obtaining equations to convert the response iterations to RT). Setting the value of the MSE to 0.0001 caused the network weights to reach an asymptotic value and as a result, it produced very similar output activations for all training m echanisms. Thus, even for the mismatch conditions in the interaction and intensity mech anisms, although the network do es not produce the correct output for high anxiety, the number of response iterations remains the same An obvious method to correct the problem is to set a higher value of the MSE as the stopping criterion during training (say 0.001). Doing so would have two main effects, (1) it would not strengthen the weights to the extent that th ey reach asymptotic valu es and so result in almost the same activation for a given input pattern under all training mechanisms, and (2) it would allow a higher margin of erro r in the network and so lead to a higher variability of performance. A higher margin of error would also allow greater increase in performance with training. Another possibl e correction is to modify the training algorithm; the current study trained the networ k using the activation values of the output units and tested it using the mechanism of collecting evidence employed by Cohen et al. (1990). Using the same mechanism for both trai ning and testing could possibly lead to a larger differential in response times. 5.1.2 Performance of the Training Mechanisms Of the three basic mechanisms used (expos ure, intensity, and in teraction), only the exposure mechanism produced results consistent with empirical findings of the dot probe task. Between the two exposure mechanisms, Exposure 3x fit the empirical findings

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127 better than Exposure 5x Thus, it may be argued that of th e three mechanisms tested in the current model, repeated exposure to negativ e stimuli best explains the etiology of attentional bias as neither of the other two training mechanisms was able to successfully elicit behavior consistent with empi rical findings of the dot probe task. The above explanation can be used as the basis for the following conclusion, “Given sufficient exposure to stimuli perceived highly threatening should cause an attentional bias towards those st imuli regardless of anxiety level ”. The statement is consistent with the models of Beck (1976) and Bower (1980) who suggested that repeated exposure to a high threat stimulus could strengthen the connections for the stimulus, thereby lowering the threshold of the activation required to elicit the attentional bias. The view is also consistent with Lang’ s biphasic theory (2000) which states that a stimulus that is rated sufficiently high in threat will cause the same effects in all individuals, regardless of a nxiety level. For high anxiety individuals, the threshold is lower than that for low anxiety individuals. According to this explanation, repeated exposure to certain stimuli could lead to th e lowering of the threshold and so produce an attention bias. The two intensity mechanisms were not ab le to correctly simulate the dot probe task as they yielded an in correct output for the mismatch conditions under high anxiety. However, both intensity mechanisms were able to produce higher activation in the output unit representing the negative picture, suggest ing the existence of a bias towards the negative image. This can be interpreted to mean that high anxiety individuals perceive the stimulus to have a higher thre at value, which causes the atte ntional bias. Further, it is clear that a higher intensity stimulus makes a larger demand on attention.

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128 The intensity and exposure mechanisms can be combined to form a new potential explanation of the etio logy of attentional bias; assume a ll individuals are low anxiety to begin with but certain individuals are repeatedly exposed to s timuli that they perceive as highly threatening. Repeated exposure to th e high threat stim uli strengthens the connections salient to that class of stimuli, effectively increasing the perceived intensity with exposure. Such a view could explain the origin of disorders such as posttraumatic stress disorder (PTSD), where individuals ar e repeatedly exposed to highly threatening stimuli in a high stress environment. In this explanation, intensity appears to be the more critical element of the two causes as indivi duals have been known to be afflicted by PTSD after being involved in one stressful s ituation, like an accident Possibly the high intensity of the stimulus causes the initial breach to attract the individuals attention. If the stimulus is sufficiently intense, it could lead to PTSD. If not, repeated exposure to the same stimulus could likely cause the onset of the disorder. A possible reason of failure of the intens ity and interaction mechanisms maybe an inadequate attention mechanism encoded in th e network, rather than shortcomings in the mechanisms themselves. Attention mechanism in this case refers to the mechanism used by the network so the network eventually at tends towards the side on which the probes appear. Indeed, if an attention mechanism can be developed that causes the network to respond with the side on which the dot appears, the two mechanisms will exhibit behavior consistent with the ex istence of an attentional bias. Further investigation using a revised attention mechanism is needed before any conclusions regarding the viability of the two mechanisms can be made. However, one unexpected observation is the similarity in th e results obtained using intensity and the

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129 interaction mechanisms, which implies that the two mec hanisms actually work in the same manner 5.2 Bayesian Network The Bayesian network (BN) model was inte nded to serve as a pr oof of concept in being able to model data pertaining to attent ional bias obtained from the dot probe. The model fell short of expectati ons and did not yield probabi listic relationships among the variables. Also, it was marred by proble ms in modeling certain conditions and interpreting the results obtained. However, the model provided some important lessons that can be relied upon to build a better mode l in the future. Three primary observations emerging from the network are as follows: 1. The conditional probability table (CPT) for attention direction (AD) was set up successfully and provided a st arting point in the attempt to quantify relationships among variables. 13. The interpretation of the probability values of variables was not clearly defined. 14. The network could not be tested against actu al data as was originally intended, in part due to very broad dichotomies used to represent the states of the variables and partly due to (2) above. As such the accu racy of the probabilistic relationships could not be verified. 5.2.1 The Conditional Probability Tables As stated in Chapter 4, one of the most crit ical elements of the BN is the CPT. The CPT encodes the probabilistic relationships among the variables. Of the five variables modeled in the BN, the most important and the only one not evident from the dot probe task is Attention Direction (AD). In fact, the primary objectiv e of the dot probe task is to infer the attention-direction of the participan t, typically done from the response time. The current study used the same principle to de rive the CPT for AD. The CPTs so obtained

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130 represent the first attempt to probabilistically quantif y the relationship among the variables of the dot probe task. The CPTs for AD highlight the difference in probability of attending towards the negative picture when the picture appears on the left as opposed to when the picture appears on the right. The main relationships represented in the CPTs of Table 4.9 are reproduced below in Table 5.1. Table 5.1. Conditional Probability Tables for variable AR for the Bayesian network. Case 1: All data Ca se 2: Data from left only Case 3: Data from right only AR= Neg Anx = High AD= Neg AD= Ntrl AD= Neg AD= Ntrl AD= Neg AD= Ntrl 1 0 0.5035 0.4965 0.5416 0.4583 0.4638 0.5362 1 1 0.5068 0.4932 0.5211 0.4789 0.4933 0.5067 The first row of the CPT can be stated as follows, “an individual with high anxiety attended to the negative pi cture appearing on the left w ith probability 0.5416 and with probability 0.4638 to a negative picture appeari ng on the right hand side”. Statistically speaking, this may not be as authoritative as st ating the main effect and interaction effects that the picture side has with the re action time, but it is certainly more discrete and quantifiable Such a representation offers an a dvantage over the more traditional method of significance testing by presenting numbers that can be compared directly against numbers obtained in similar fa shion from other studies. Despite the fact that the probabilistic rela tionships encoded in the CPT could not be tested against real data, the manner in wh ich they were computed is logical and straightforward, and lends itself to discretizat ion of the relationships. The relationships established were used to infer the probability of AD=Neg for an individual with known anxiety. For row 3 of Table 4.10 (a), (reproduced below as Table 5.2) the probability of AD=Neg increases from 0.5026 to 0.9506 indicating the likelihood that an individual

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131 known to be highly anxious will attend towards the negative image given PS=Neg (probe replaces negative image) and RT= low The arousal rating of an image required to grab the participants attention 95% of the time is given by the posterior probability of AR=Neg= 0.503 (up from 0.5). Rows 3 through 6 (sha ded) in Table 5.2 depict the two possible conditions ( PS=Neg, RT=low & PS=Ntrl, RT=low ) for Anx= high and Anx= low The rows can be interpreted as follows: 2. Row 3. Given the observations that the probe replaces the negative image and the recorded RT is low an individual with high anxiety will attend to a negative picture with normalized arousal rating= 0.503 with probability = 0.9506 15. Row 4. Given the observations that the probe replaces the neutral image and the recorded RT is low an individual with high anxiety will attend to a negative picture with normalized arousal rating= 0.4969 with probability = 0.0506 The decrease in the probability of AD=Neg is inferred from an apparent attention towards the neutral image. The inference may not appear to be consistent with the findings of the dot probe task (an individual with high anxiety attending to th e neutral picture) but it should be noted that the network re flects the changes in probabilities given the observations. The observation in this case already points to a higher response time ( RT=high ) for the dot replacing the negative image. Thus, this condition can be used to answer the question, “What is the probability that an individual with high anxiety attends to the negative imag e given that the individual records a high RT for when the dot replaces the negativ e image? Also what is the normalized arousal rating of the negative image?” 16. Row 5. Represents the same observations as Row 3 but for a low anxiety individual. As can be se en, the probability of AD=Neg decreased slightly, coupled with a decrease in the posterior probability of AR=Neg Similarly, rows 7 and 8 show inference of attention direction a nxiety level of the individual given a high arousal rating. It should be noted that the values oscillate around 0.95 and 0.5 as these were the values set for RT given AD and PS in the CPT for RT (see Table 4.15.

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132 Table 5.2 Posterior probabilitie s of various variables com puted given the evidence (in bold) using the CPT derived from all data AR= Neg AD=Neg Anx=high PS=Neg RT=low Prior Post Prior Post Prior Post Evidence Evidence 0.5 0.5023 0.5026 0.9505 0.5 0.5007 1 1 0.5 0.4977 0.5026 0.0505 0.5 0.4993 0 1 (row 3) 0.5 0.503 0.5026 0.9506 1 NA 1 1 (row 4) 0.5 0.4969 0.5026 0.0506 1 NA 0 1 (row 5) 0.5 0.5016 0.5026 0.9503 0 NA 1 1 (row 6) 0.5 0.4984 0.5026 0.0503 0 NA 0 1 1 NA 0.5026 0.951 0.5 0.5015 1 1 1 NA 0.5026 0.051 0.5 0.4985 0 1 5.2.2 Interpretation of Probability Values A major shortcoming of the model was the l ack of rules to interpret the probability values for all of the variables. Interpretation of the independent vari ables of the dot probe task was fairly straightforward; anxiety re presented the normalized score obtained on the STAI-Trait, while Arousal Rating depicted the normalized IAPS arousal rating of the image. The ambiguity in interpretation arose in Attention Direction ; for example, what does a value of AD(neg) = 0.75 specify? The participant devoting 75% attentional resources to the stimulus or does it predict the probability of the participant attending to the negative stimulus of give n arousal rating? The latter is akin to establishing a likelihood of attention directi on towards the negative stimulus. In either case, the interpretation must be clearly established be fore the results of the modeling with the BN can be used to establish robust relationships. 5.2.3 Testing Against Actual Data All the variables used in the network had only two possible states (true and false) resulting in an overall lack of accuracy as adding ev idence to the network became virtually impossible. It may be recalled that adding evidence to a variable in a BN means that the state of the variable is known with certainty (i.e., the probability of the variable

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133 being in the given state is 1) Clearly, using broad dichotomie s, such as a variable being very high negative or neutral in arousal, or an individual being only high or low in anxiety does not reflect actual conditions. For instance, if th e median anxiety score is 37, classifying an individual with anxiety score of 38 as high anxious may not be accurate for the indibvidual. It was believed that the netw ork could be tested for any probability of a given variable by setting its prior probability. However, when the prior probability was set in such a fashion, the network computed a posterior probability of the variable as well. The posterior probability represented a change in the state of the variable, which negates the fact that the variable is fixed in a given state. Fo r clarification, consider Table 4.11 (a) and Table 4.11 (b). Table 4.11(a) re presents an attempt to compute the posterior probability of Anxiety = high and AD= Negative for various values of AR of the image. As can be seen, the networks computes the posterior probability AR also, which makes the results ambiguous; it cannot be stated that the values of AD and Anxiety are representative of an image of arousal ra ting 0.25. There is no cl ear cause and effect. Similarly, in Table 4.11 (b), the same happens with Anxiety An obvious solution is to increase the numbe r of possible states of the variables of the network. For example, Anxiety could be specified in terms of quartiles or decitiles of the STAI score. This would allow adding ev idence to the network and observing a clear effect (change in AD and AR ) of the cause (specifying Anxiety ). Continuing with this line of reasoning, setting states for AD and its implication must be clearly formed. 5.3 Statement of Limitations Both the NN model and the BN model suffered from two limitations, one due to their nature (and therefore not unique to the current study), while the other directly referred to the extent to which the ne tworks modeled the dot probe task.

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134 The first limitation of the NN stemmed fr om the fact that NN are capable of modeling any problem domain when given the appropriate training. As a result, appropriate training is a cri tical aspect of a modeling using a NN. The current study attempted to model human performance on th e dot probe task. A limitation of the study was in encoding the attention mechanism into the network. Essentially, the network was allowed to learn the attention mechanism from increased traini ng to attend to the side on which the probe appeared. This training does not reflect the atten tional mechanism used by human participants; where an individual actively and delibe rately searches for the dot probe when the probe does not appear in th e spatial location being attended to. Another limitation was the lack of ability to present the images for a certain amount of time and have the dot appear following image offset. This potentially limits the extent to which the task is modeled by the NN as the network applies the activation due to probes to the network without removing the activation due to the stimuli, which is contrary to the actual task. Additionally, the NN was limited in its ability to produce generalizable results due to its inability to present results in terms of RT. The main inherent limitation of the BN m odel was they are based in probability theory, and so must obey the laws of proba bility. This limits the application of the network, specifically when supplying the conditional probability for Arousal Rating Although AR=Ntrl was possible in the network, the BN could not be configured to handle such a condition as one image of the networ k was assumed to be neutral and the other was assumed to be negative. AR represented the normalized arousal rating of the negative image; so AR=Ntrl meant that both the displayed images were neutral. This information was inconsistent with information listed in the CPTs of other variables.

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135 5.4 Future Research The current study represents the first app lication of NN and BN to the dot probe task. Although both models represent a significant first step in the pr ocess of establishing robust models to model the dot probe task, much work is required before they can yield relationships among the variab les of the task and insight s into its mechanisms. For the NN, the first step should be to set a reliable at tentional selection mechanism. The training processes used to trai n the network also need to be revised so as to yield a larger difference in the number of response iterations. Once these conditions have been met and a working NN is in place, it can be used to derive a relationship between the anxiety and RT by using normalized anxiety scores to set the activation for the anxiety units in much the same that anxi ety scores were used to set the conditional probabilities of the BN. Unlike the NN, which has been accepted in to psychological research, BN are as yet untested in the area. They also suffer from the disadvantage of being associated with the stigma of the word “probability”. Consequently research is required to highlight the ease of use of such models along with their potenti al advantages. The first step in highlighting the potential advantages involve s using the network to set probabilistic relationships among the variables of the task by extending the model used in the current study and adding finer divisions of states for the variables. Once such relationships are established, more variables can be added to the BN. For example, a BN can be developed to account for the relationship between arousal rating of a picture and its perc eived arousal rating based on the anxiety of the individual. At this point, it should be reit erated that BN will not yield conclusions about data, instead a BN will yield potential relationships that can then be tested by actual studies.

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136 5.5 Summary and Conclusion Both the NN and the BN models met with mixed success and shortcomings but provided important insights into the mechanis ms of attentional bias as measured by the dot probe task. Also, neither model was completely accurate, with the NN being riddled with problems with the atte ntional mechanism while the BN was plagued by a broad categorization of variables states. The NN was not able to establish a robust set of relationships to translate the number of iterations required to produce th e response to the RT. Ho wever, the number of response iterations themselves was representa tive of RT consistent with the hypothesis for the NN. The BN model also could not establish a robust set of probabi listic relationships between the variables. Howeve r, the model strongly indicated the existence of such relationships among the variables. Additionall y, the model highlighted the importance of establishing the relationships and fu rther, verifying their accuracy. Summarizing, the two models provided important insights in to the potential mechanisms and relationships that exist among the variables of the network. The NN offers a simple and elegant medium to simulate performance and estimate the inner workings from the connection weights and performance of the network. The BN lends itself well to form a common ground to compare results from various studies and so form robust relationships. Last but not least, it should be mentioned that modeling with two networks is becoming increasingly simple with the availability of software packages (such as PDP++ for NN and Microsoft’s MS BNx and the Bayes Net Toolbox for Matlab by Kevin Murphy) and for the two available free of cost for research purposes.

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137 APPENDIX WEIGHTS AND BIASES OF THE NEURAL NETWORK MODEL Input 1 Input 2 Input 3 Input 4 Input 5 Input 6 Input 7 Input 8 Hid 1 -0.8194-0.4376 -0.44140.5418 0.0397 0.2172 0.8931 0.3169 Hid 2 2.5209 1.7427 2.0858 -0.0680 -0.219 3-2.8738 -2.4553 -2.1877 Hid 3 5.9539 5.5501 5.0023 0.4513 0.6929 -5 .8293 -5.0641 -4.8331 Hid 4 -0.9535-1.1615 -0.84330. 1623 -0.33980.3045 0.6285 0.8757 Hid 5 -2.4844-2.4792 -2.02400 .2296 0.1312 2.3250 2.1204 1.5140 Table A-1. Weights between the input and hidden units after training for baseline mechanism Input 1 Input 2 Input 3 Input 4 Input 5 Input 6 Input 7 Input 8 Hid 1 -2.1930 -0.8497 -3.2215 -1 .2682 -0.28720.9026 1.3947 0.5475 Hid 2 4.9266 2.2117 5.9993 -1.2224 -0.973 3-7.4268 -5.6760 -3.7501 Hid 3 13.1477 7.4207 14.9115-2.1814 -1. 2797-13.3303 -13.1663 -10.4007 Hid 4 -1.8200 -1.1174 -2.5289 -1.267 8 -0.8611-0.9807 -0.2389 0.6141 Hid 5 -6.6953 -3.7033 -7.975 6 0.6873 0.5719 6.9302 6.1968 3.7711 Table A-2. Weights between the input and hidden units after training for exposure 3x mechanism Input 1 Input 2 Input 3 Input 4 Input 5 Input 6 Input 7 Input 8 Hid 1 -0.75700.1512 -0.8906-2.3080-0. 3927-2.9407 -1.1205 -0.5194 Hid 2 4.45641.1325 5.82630.0009-0.58317.7683 -4.6599 -1.6034 Hid 3 13.44613.2944 16.282-1.96491.4307 -13.8215 -20.9822 -5.8300 Hid 4 1.76740.2543 1.7297-1.2275-0.801 7-5.4881 -3.5621 -0.9221 Hid 5 -5.1677-3.7056 -5.4234-0. 1136-0.49835.8968 5.9031 0.6683 Table A-3. Weights between the input and hidden units after training for exposure 5x mechanism Table A-4. Weights between the input and hi dden units after trai ning for interaction mechanism Input 1 Input 2 Input 3 Input 4 Input 5 Input 6 Input 7 Input 8 Hid 1 4.2775 2.6037 -0.6581 3.8386 -0 .44060.8520 -8.0108 4.9827 Hid 2 4.2439 -7.0913 2.3614 1.1966 -5. 9925-3.1982 -8.3749 6.3344 Hid 3 -0.3593 12.1168 5.0171 8.1138 -6 .5934-5.8875 -10.7942 1.0197 Hid 4 -0.9166 -0.8082 -0.8608 -1.009 7 -1.91570.9117 -1.1597 -0.4743 Hid 5 -6.3304 2.4107 -2.2118 2.8539 -6.25514.9199 1.0390 -2.2105

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138 Table A-5. Weights layer 2 (between the hi dden and the output units) after training for baseline mechanism Table A-6. Weights layer 2 (between the hi dden and the output units) after training for exposure 3x mechanism Hid 1 Hid 2 Hid 3 Hid 4 Hid 5 Out 1 -3.30758 7.29696 17.1209 -2.11781 -10.4691 Out 2 1.49286 -6.46894 -17.5494 1.18319 7.48194 Table A-7. Weights layer 2 (between the hi dden and the output units) after training for exposure 5x mechanism Hid 1 Hid 2 Hid 3 Hid 4 Hid 5 Out 1 -1.05497 5.7585814.79331.9961 -7.01226 Out 2 1.51735 -4.04257-16.831-1.3786 6.70004 Table A-8. Weights layer 2 (between the hi dden and the output units) after training for interaction mechanism Hid 1 Hid 2 Hid 3 Hid 4 Hid 5 Out 1 -8.74957 6.29904 9.06092 -0.79573 -8.92881 Out 2 8.65513 -6.47485 -8.91653 0.873517 8.85659 Table A-9. Biases for hidden units for all training mechanisms Hid 1 Hid 2 Hid 3 Hid 4 Hid 5 Baseline -0.7642 -0.1195 0.6912 -0.4025 0.0630 Exposure 3x -3.91226 -2.66741 -1.50587 -5.3248 -0.38503 Exposure 5x -6.56968 -1.56829 2.30081 -5.47391 -0.73735 Interaction 3.5541 -4.67681 1.02403 -2.56079 -1.29189 Table A-10. Biases for the output un its for all training mechanisms. Out 1 (Left) Out 2 (Right) Baseline -2.8754 2.7568 Exposure 3x -12.0748 3.25915 Exposure 5x -10.2105 8.34891 Interaction 4.10617 -4.09197 Hid 1 Hid 2 Hid 3 Hid 4 Hid 5 Out 1 -1.4613 3.1089 10.0525 -1.8728 -4.0868 Out 2 1.4282 -3.7617 -9.9330 1.9455 4.1715

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148 BIOGRAPHICAL SKETCH I began my professional educational caree r at the Regional Engineering College (REC) at Jalandhar in India, pursuing my Bachelor of T echnology in computer science and engineering. REC did not have any basket ball facilities. I ha d always considered myself an athlete and a basketball player befo re a student, so I transferred to Guru Nanak Dev University (GNDU), Amritsar, India, where I led the University basketball team to second place at the All India Inter University Basketball Championship. While at GNDU, I came upon a book on sport psychology that featured an article on the use of imagery (specifically a techni que called visuomotor behavior rehearsal (VMBR). The book was my first brush with th e field of Sport Psychology. I graduated from GNDU at the top of my class in 1999. In Fall of 2000, I started my master’s progr am in computer engineering. Here I met Dr. Anand Rangarajan and my fascination wi th neural networks and other tools for reasoning under uncertainty flourished. At the sa me time, I did not feel at home in the field of computer engineering. In Spring of 2002, I met with Dr. Christopher Janelle to explore my options for doing a Master’s in mo tor learning and control. The rest, as they say, is history. I found the missing element fr om my career. I am now looking forward to graduating and develop software to enhance human performance and better lifestyle.


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Physical Description: Mixed Material
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COMPUTATIONAL ACCOUNTS OF ATTENTIONAL BIAS: NEURAL NETWORK
AND BAYESIAN NETWORK MODELS OF THE DOT PROBE PARADIGM













By

AMITOJ SINGH LIKHARI


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE IN EXERCISE AND SPORT SCIENCES

UNIVERSITY OF FLORIDA


2005

































Copyright 2005

by

Amitoj Singh Likhari

































This thesis is dedicated to my family, especially my Dad, Sarab Jit Singh, who always
pushed me to follow my heart and gave me the reason to pursue this Master's. My Mom,
Sukhjinder, who patiently supported me through every step of the way. My sisters,
Tanvir and Kamalpreet, and my brothers-in-law, Parneet and Dhananjay, for helping and
guiding me find what I truly believe in. Last but not least, my three nephews, Sukhsahegj,
Sarguun and Manu, for making me realize that things were not that bad after all.















ACKNOWLEDGMENTS

Countless hours have gone into the preparation of this thesis. However, I could not

have made it if I did not have people pushing and prodding me to do better. I would like

to thank Dr. Christopher Janelle, my advisor, for helping and supporting the idea of my

thesis even when it was not as concrete, and for letting me down easy on the numerous

occasions that I presented him with what surely must be the worst writing possible. I

would also like to thank my friends and peers at the Motor Behavior Laboratory at the

University of Florida, Steve Coombes, without whose data and revisions to text, this

work not have been possible, and Sarah Huie, for proofreading my first drafts and going a

long way in improving the quality of this work. Special thanks go to Dr. Anand

Rangaraj an, Associate Professor at Computer and Information Science and Engineering,

at the University of Florida, for helping me solidify the concepts and asking me questions

to force me to think clearly. Over the last few weeks, I have spent a significant amount of

time at the library, and I thank the one person who agreed to study there with me, Angela

Duke. Finally, none of this would not have been possible if Aaron Duley, also of the

Motor Behavior Laboratory., had not first suggested the idea of developing a computer

simulation.
















TABLE OF CONTENTS

page

A C K N O W L E D G M E N T S ................................................................................................. iv

LIST OF TABLES ............... .............. ......................... ............... ix

LIST OF FIGURES ......... ......................... ...... ........ ............ xi

ABSTRACT .............. ............................................. xii

CHAPTER

1 IN TR OD U CTION ............................................... .. ......................... ..

1.1 Cognitive M odels of Anxiety .............................. ................. .. ....... ................2
1.2 Computer Tools to Investigate Mechanisms of Attentional Bias...........................4
1.2.1 N eural N etw orks............ .... ...................................... .... ................... .. 4
1.2.2 B ayesian N etw orks ......................................................... .............. 5
1.3 P reviou s R research ............ ... ........................................................ ........ ... ...
1.4 L im station s ...................................... ............................... ................ .. 9
1.5 Statem ent of P rob lem ............................................ ......................................... 10
1.6 Statem ent of P purpose ............................................................................ .... .......10
1.7 Current Study ................................. ........................................ ......... 10
1.7.1 Objectives of the Neural Network Model ..................................................11
1.7.2 Objectives of the Bayesian Network Model.............................................. 12
1.8 H y p oth eses............................. ....................................................... ............... 12


2 REVIEW OF LITERATURE ........................................................ ..............14

2 .1 A n x ie ty ........................................................................................................... 1 5
2.2 Attentional Bias .............. ........ .. ...............................22
2.2.1 Dichotic Listening Paradigm ....................................... ...............23
2 .2 .2 Stroop T ask .................................................................. 24
2.2.3 D ot Probe Task ................................................ .. .... .... ................. 29
2.2.3.1 Initial studies (basic dot probe task).........................................30
2.2.3.2 Manipulation of stimulus duration .............................................37
2.2.3.3 B ackw ard m asking ................................... ..................................... 38
2.2.3.4 Pictorial dot probe task.................................... ...... ............... 39
2.2.3.5 Social anxiety ....................................... ........ ........ ......42


v









2 .2 .3.6 D rug abu se............ .............................................. .... . .......... 44
2.2.3.7 Sm oking and alcoholism ...................................... ............... 44
2.2.3.8 Eating disorders ................................................... ............... 45
2.2.3.9 Pain and miscellaneous areas ............... ................................. 46
2.2.3.10 Limitations of the dot probe.........................................................46
2.3 Connectionist M odels of Attention.................................................................... 46
2 .3.1 N eural N etw orks............ .... .......................................... ........ ........... 48
2.3.1.1 O verview ................................................................ ........... .48
2 .3 .1 .2 L e arn in g ..................................................................................... 4 9
2.3.1.3 Supervised learning. .......................................................................50
2.3.1.4 An example of supervised learning...............................................50
2.3.2 D details and Theory .................................. .....................................51
2.3.2.1 Overview .............. ......... .......................................... ......... 51
2 .3.2 .2 N rotation .......................................................... .. .......... 53
2.3.2.3 Initialization ......................................... .................. ......54
2 .3.2 .4 N ode D etails............ .... .................................... .... .... ........... 54
2.3.2.5 Net input ............... ............ ............................54
2.3.2.6 A ctivation level ............................ ................... .. ...... .... 55
2.3.2.7 O utput................................................... 56
2 .3.2 .8 T raining ................................................ ............... 57
2.3.2.9 Testing ............. ......................................... ............... .... 59
2.4 Connectionist Models of the Stroop Task ...........................................................59
2.4.1 The C ohen M odel ............................................... ............................ 59
2 .4 .1.1 S tru ctu re .............................................. ................ 6 0
2.4.1.2 Initialization ......................................... .................. ......60
2.4.1.3 Net input ............................................................. 61
2 .4 .1.4 A ctiv ation ......................................................... .. .......... ...... 62
2.4.1.5 Output ............................. .... ............... 62
2 .4 .1.6 T raining ................................................ ............... 63
2.4.1.7 Testing ................ ........... ...... ................... 64
2.4.1.8 Sim ulations and results............................................... 65
2.4.2 The M atthew s and H arley M odel ........................................ .............. 66
2 .4 .2 .1 H y p oth eses ................................................................................. 6 7
2 .4 .2 .2 S tru ctu re ..................................................................................... 6 8
2.4.2.3 Initialization ................. ............. ...................69
2 .4 .2 .4 In p u t ........................................................................................... 6 9
2 .4 .2 .5 O u tp u t ......................................................................................... 6 9
2.4.2.6 Training and testing................................................. 69
2.4.2.7 Results ...................... ...................... ......... 72
2.4.3 Pros and cons of using PDP models ................. .... .................. 73
2.4.3.1 A advantages ......................................................... .............. 73
2 .4 .3.2 C criticism s .............................. .................. .. ................. 73
2.5 A Belief Network Model of Attentional Bias in Dot Probe Paradigm ..............74
2.5.1 N nothing is C certain ......................................................................... 75
2.5.2 Axiom s of Probability .............. ............ ...... ..... .... ................. 77
2.5.3 Law of Total Probability ................................... ...................78









2.5.4 Conditional Probability ............................................ ............... 80
2 .5.5 C hain R ule ....................................................... 80
2.5.6 B ayes' Theorem .......................... .. .. ................ ...... .. .. ...... .. 81
2.5.7 Conditional Independence.................. ................. ..... ............... 82
2.5.8 G raphical N otation ........................................ ......................... 83
2.5.9 Causal Networks and d-separation................................. ... ...............84
2.5.10 B ayesian N etw orks................................................. ........................ 85
2.5.11 An Example of a Bayesian Network.............................................90
2 .6 Sum m ary ................................ ................. .............................. 94


3 M E T H O D S ........................................................................................................... 9 5

3.1 The Task ...................................................................... ........... ........ 96
3.2 Neural Network Model of the Dot Probe task................................... ................96
3.2.1 M mechanism s ......... ...... ........................ ........ ........ .. .. .. ........ .... 97
3.2.1.1 Baseline condition ............... ........... .. .....................99
3.2.1.2 Exposure mechanism.........................................................99
3.2.1.3 Interaction m mechanism ...................................... ............... 100
3.2.1.4 Intensity condition................................................101
3.2.2 Sim ulations ......... .. .... ....................................... 102
3 .2 .3 Stru ctu re ..............................................................10 2
3.2 .4 N et Input ......................................................................................... ......103
3.2.5 A ctivation ......................................... ................... .... ...... 103
3 .2 .6 O u tp u t ................................................................................................. 1 0 4
3.2.7 Initialization...................................... ...............105
3 .2 .8 T ra in in g .............................................................................................. 1 0 5
3.2.9 Testing ..................................................................... ........ 105
3.3 B ayesian N etw ork ..................................................................... 105


4 R E S U L T S .......................................................................................1 10

4.1 Neural Network Model ........................................................ 110
4.1.1 Results for Simulation 1: RT .............. .................. ...............113
4.1.2 Results for Simulation 2: A ctivation ................................. .................117
4.2 Bayesian N network M odel ............................................................. ............. 119


5 D ISC U S SIO N ...................................................... 124

5.1 N eural N etw ork M odel .......................................................................... ... ..........124
5.1.1 W eights of the Network ................................................ ....... 125
5.1.2 Performance of the Training M echanism s ...............................................126
5.2 Bayesian Network .......................... .. ............... 129
5.2.1 The Conditional Probability Tables.................................. ........... ....129
5.2.2 Interpretation of Probability Values ........................... ................. 132









5.2.3 Testing Against A actual D ata ....................................... ............... 132
5.3 Statem ent of Limitations..................... ...................................... 133
5.4 Future R research .................. ..................................... .. ........ .... 135
5.5 Sum m ary and C onclusion........................................................ ............... 136


APPENDIX

WEIGHTS AND BIASES OF THE NEURAL NETWORK MODEL...........................137

L IST O F R E FE R E N C E S ......... .. ............. .............................................................. 139

B IO G R A PH ICA L SK ETCH ............ .................................................... .....................148
















LIST OF TABLES


Table pge

2.1 Input patterns and corresponding outputs used for training the network by Cohen et
al. (19 9 0 ) ............................................................................ 6 4

2.2 Training patterns and number of times each condition was presented to the network to
train for the em otional Stroop task ........................................ ........ ............... 71

3.1 Training patterns used to train the NN for baseline, exposure 3x and exposure 5x
c o n d itio n s ......................................................................... 9 8

3.2 Training patterns for the attention mechanism for baseline, exposure 3x and exposure
5x con edition s. ...................................................... ................. 9 8

3.3 Training patterns used to train the network for the interaction mechanism. ...........101

4.1 Number of training iterations and MSE for each training mechanism.....................110

4.2 Basic test patterns for the neural network model....... ..................................112

4.3 Test patterns for the intensity condition............................... .... ............... 112

4.4 Results of Simulation 1 under conditions of high anxiety..................................... 114

4.5 Results of Simulation 1 under condition of low anxiety.................. .. .................115

4.6 Simulation 2: Output activations for high and low anxiety ................................... 118

4.7 Conditional probability tables for variables Arousal Rating (AR), Anxiety (Anx),
Probe Side (PS), and Reaction Time (RT).................................... ..................... 120

4.8 Conditional probability tables for variable AR for the Bayesian network. .............120

4.9 Posterior probabilities of various variables computed given the evidence (in bold)
using the CPT derived from all data ..................................... ......... ............... 121

4.10 Posterior probabilities of various variables computed given the evidence (in bold)
using the CPT derived from data using pictures appearing on the left only. ........ 121

4.11 Posterior probabilities of various variables computed given the evidence (in bold)
using the CPT derived from data using pictures appearing on the left only..........122









4.12 Prior and posterior probabilities for various prior probability values ofAR= Neg. 122

4.13 Prior and posterior probabilities for various prior probability values ofAnx= high122

4.14 Prior and posterior probabilities ofAnx= high for various prior probability values of
AR N eg givenAD neg. .......................... ...... .................................... 123

4.15 Prior and posterior probabilities ofAR= Neg for various prior probability values of
Anx high given AD neg. ............................................. ............................ 123

5.1 Conditional Probability Tables for variable AR for the Bayesian network.............130

5.2 Posterior probabilities of various variables computed given the evidence (in bold)
using the CPT derived from all data.................................... ....................... 132

A-i Weights between the input and hidden units after training for baseline mechanism 137

A-2 Weights between the input and hidden units after training for exposure 3x
m mechanism ..................................... ................................ ......... 137

A-3 Weights between the input and hidden units after training for exposure 5x
m mechanism ..................................... ................................ ......... 137

A-4 Weights between the input and hidden units after training for interaction mechanisml37

A-5 Weights layer 2 (between the hidden and the output units) after training for baseline
m mechanism ..................................... ................................ ......... 138

A-6 Weights layer 2 (between the hidden and the output units) after training for exposure
3x m ech an ism ................................................. ................ 13 8

A-7 Weights layer 2 (between the hidden and the output units) after training for exposure
5x m ech an ism ................................................. ................ 13 8

A-8 Weights layer 2 (between the hidden and the output units) after training for
interaction m ech anism .............................................. ........................................ 13 8

A-9 Biases for hidden units for all training mechanisms.....................................138

A-10 Biases for the output units for all training mechanisms. ......................................138















LIST OF FIGURES


Figure pge

2.1 Cognitive mechanisms underlying biases in initial orienting to threat in anxiety.......19

2.2 V versions of the Stroop task. ...............................................................................25

2.4 A general multi-layer backpropagation neural network. ...........................................53

2.5 Details of a simple processing unit of a neural network...........................................55

2.6 Graph of the logistic sigmoid function ...........................................................56

2.7 Flow of activation (solid lines) and error (dotted lines) in a multi-layer
backpropagation neural network. ........................................................................... 58

2.8. Neural network model for simulation of the Stroop task.......................... .........61

2.9 Matthews and Harley Model (a) the first two models. The dotted lines were connected
in Model 2 while non-existent in model 1, (b) model 3 shared the same connections
for the 2nd weight layer with model 1. Connections that differ in layer 1 are shown
as solid lines while those carrying over from 1 and 2 are shown in dotted lines.....70

2.10 d-separation in (a)serial, (b) diverging and (c) converging connections .................87

2.11. Illustration of conditional independence relationships. .........................................89

2.12 A Sample Bayesian network to determine model the probability of the grass being
wet given states of cloudiness (C), Rain (R) and Sprinkler (S).............................92

3.1 Neural network model for simulating dot probe task. .............................................104

3.2 Bayesian network model of the dot probe task ............ ........................ .................. 108















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science in Exercise and Sport Sciences

COMPUTATIONAL ACCOUNTS OF ATTENTIONAL BIAS: NEURAL NETWORK
AND BAYESIAN NETWORK MODELS OF THE DOT PROBE PARADIGM

By

Amitoj Singh Likhari

May 2005

Chair: Christopher Janelle
Major Department: Exercise and Sport Science

Anxiety disorders afflict roughly 19 million American adults and their treatment

costs upwards of 40 billion dollars annually. Attentional bias is believed to play a critical

role in the etiology and maintenance of such disorders. The dot probe paradigm is used to

measure attentional bias. In order to develop better treatment protocols, it is essential to

understand the mechanisms of attentional bias.

The current study attempted to simulate human performance on the dot probe task

using a neural network (NN) and compare three potential mechanisms of attentional bias.

The NN accurately simulated performance for one of the mechanisms called the exposure

mechanism. The mechanism successfully produced an attentional bias in the network by

repeatedly applying negative inputs to it under conditions of high anxiety. The other two

mechanisms tested were based on the interaction hypothesis and intensity mechanism.

The latter explains occurrence of attentional bias through a increased in the perceived









threat value of salient stimuli by high anxiety individuals. The model also indicated a

need to create a mechanism to simulate deliberate attention.

The second part of the study consisted of building a probabilistic model of

attentional bias in the dot probe task using a Bayesian network (BN) to uncover

probabilistic relationships among the variables. The network was able to partially model

the relationships among the variables. However, it proved to be unfit in its current form

for the task; finer divisions are required to model data more accurately in the BN. On the

whole, the model met with limited success but offered important insights and lessons that

can be applied to building better models in the future.














CHAPTER 1
INTRODUCTION

Anxiety is typically considered a negative emotion that adversely affects the ability

to attend to salient information required to complete tasks at hand (Woodman & Hardy,

2001). Distraction due to anxiety can affect the information processing system to an

extent that the affected individual cannot perform tasks efficiently. Such a condition

characterizes a wide spectrum of anxiety disorders. Anxiety disorders are currently the

most common mental illness in the United States today. According to the latest

information available on the website of the Anxiety Disorder Association of America

(ADAA, 2004), over 19 million adult Americans currently suffer from some form of

anxiety disorder. Over 80% of these adults are afflicted by two specific disorders,

namely, Generalized Anxiety Disorder (GAD) and phobias. These two disorders are

twice as likely to occur in women than men. On the whole, treatment costs for anxiety

and related disorders approximate to $42 billion dollars a year. Clearly, a strong need

exists to understand the nature and mechanisms of these disorders to devise better

treatment protocols.

Anxiety affects an individual's ability to attend to task relevant cues in requisite

detail by diminishing attentional resources available. Levels of trait anxiety reflect the

propensity of a person to experience anxiety in a wide range of contexts, whereas state

anxiety refers to the susceptibility to experience higher levels of anxiety in a given

situation. Typically, individuals high in trait anxiety experience higher levels of state

anxiety.









Anxiety influences the direction of attentional allocation and how one processes

information. Specifically, anxiety influences attentional bias, which is defined as a

discrete shift in attention to some change in the environment that is brought about either

voluntarily or involuntarily (though typically the former) (Williams, Watts, MacLeod &

Matthews, 1997). According to some cognitive models, an attentional bias towards threat

related information plays an important role in etiology and maintenance of anxiety

disorders.

1.1 Cognitive Models of Anxiety

Two such cognitive models are Beck's schema theory (Beck, 1976; Beck, Emery &

Greenberg, 1986; Beck et al. 1979) and associative network model of Bower (Bower,

1981). Both were among the most popular models until the middle of the 1980's. Beck's

schema theory proposed that all information was processed according to a set schema. In

anxiety disorder, the schema related to the processing of negative information became

dysfunctional, thereby leading to selective processing of only negative information. This

formed a cycle, with attention to (negative) threat related information strengthening the

schema, thereby rendering the individual unable to avoid attending to such information.

Bower (1981) explained the same using an associative network. He posited that

information was stored in an associative network, with memories of events linked to

emotions they evoke and vice versa. According to Bower, anxiety caused an attentional

bias towards threat. That is, nodes linked to threat information were activated more

strongly and more frequently than others, leading to strengthening of the connections

between nodes representing that class of information. The increase in connection strength

resulted in even small activation of a node having a large overall effect. In other words,









cues having a higher level of perceived threat demanded a larger share of attentional

resources.

Both models suggested attentional bias as the primary driving force responsible for

causing and maintaining anxiety disorders. Both models however, incorrectly predicted

an attentional bias toward information concerning loss or failure among depressed

individuals. Williams, Watts, MacLeod and Matthews (1987) attempted to rectify this

erroneous model by suggesting that anxiety is linked to an attentional bias towards threat

information while depression is similarly biased towards recall of information related to

loss or failure and as such is unaffected by the level of anxiety of the individual. They

claimed that attentional bias was a product of the level of trait anxiety and the perceived

threat value of the information. High trait anxiety individuals orient toward the threat

stimulus while low trait anxiety individuals attend away from it.

The main emphasis of research to date has been to understand causes and

mechanisms of attentional bias. Causes include such attributes as the situation in which

bias occurs, the threat value of the stimulus, trait and state anxiety levels of the person.

Investigations into the causes are typically carried out by experimentation, using

paradigms such as the dichotic listening paradigm, the Stroop task, the dot probe and the

visual search paradigm to observe and understand the nature of attentional bias in various

situations. Mechanisms, on the other hand, refer to how the bias occurs and the location in

the information processing system on which it acts (Williams et al., 1997). Typically,

mechanisms are determined by formulating theories and models of attentional bias and

verifying their correctness.









1.2 Computer Tools to Investigate Mechanisms of Attentional Bias

1.2.1 Neural Networks

A promising method that has been used to better understand the mechanisms is by

modeling tasks that measure attention. A popular tool for constructing such models is a

neural network. A neural network (NN) (or Parallel Distributed Processing (PDP)

network) is a modeling method conceptually based on the functioning of the brain. NN

models attempt to computationally mimic the massive parallelism inherent in the

structure of the brain. A NN model essentially consists of a number of processing units

connected with each other with either excitatory or inhibitory connections, thereby either

increasing or decreasing activation levels of other processing units with which they

articulate. The processing units themselves are constant, in that each unit performs the

same computation. The critical element influencing the output of the network is the input

to each unit. The input to a unit depends upon the weights on the connections between the

unit in question and other units. As such, changes made to weights in the network affect

the input to each unit, and ultimately the output of the network. Learning in the context of

NN consists of determining the correct weight for each of the connections to accurately

model the observed data from the problem domain.

Learning in NN is essentially dichotomized into supervised and unsupervised

learning. The model used in the present study follows supervised learning. Specifically,

the network has to be "trained" with known data. Training in this context consists of

supplying input with known output to the network. Weights on the connections between

units are then adjusted until the network yields the correct output for the given input

pattern. This cycle is repeated on a large number of input patterns, until the network









produces the correct output to all training patterns. Details of this process are provided in

the Chapter 2.

One main advantage of using NNs to model cognitive phenomena is that they offer

a precise, computational account of the observed phenomenon consistent with the

parallelism in the brain. Another advantage is in the ability of NN to handle unknown

data and situations using data from known situations and data, thus allowing statistical

regularities to emerge without requiring explicit coding (Matthews & Harley, 1996).

1.2.2 Bayesian Networks

A second method of modeling that has been gaining popularity in artificial

intelligence and other industrial and statistical modeling settings but has not been used in

anxiety research, is constructing probabilistic models of the variables involved in a task.

The present study marks the first attempt to develop a probabilistic model of attentional

bias using Bayesian networks (BN). BN allow intuitive probabilistic modeling of

problem domains in which the relationships between variables are clearly understood.

Such models rely on the laws of probability coupled with subjective probabilistic

relationships to perform probabilistic inference, from a quantitative standpoint. Although

the study of attentional bias has matured to the point where these relationships have been

empirically delineated, no attempt has been made to quantify these relationships.

1.3 Previous Research

The Stroop task (Stroop, 1935) has traditionally been the most popular choice for

studies investigating attentional bias. Words are presented in different colored inks, with

the participant being required to perform one of two tasks, color naming (naming the

color of the ink) or word reading (reading the word out loud). Typically, color naming is

slower than word reading in conflicting conditions (i.e., when the word represents the









name of a color different than the ink (Cohen, Dunbar & McClelland, 1990)). A generally

accepted explanation is that because word reading is a more automatic task than color

naming, the content of the word interferes with processing information regarding color,

and so causes the delay (Dyer, 1973; Glaser & Glaser, 1982). This robust finding has

become commonly known as Stroop interference.

The emotional version of the Stroop task involves presentation of an emotional

word instead of neutral words or color names. Color naming is slower for emotional

words than for neutral words in this version. Interference in the modified Stroop task is

explained as occurring due to the amount of effort required to shut-out the content of the

word, leaving fewer processing resources to perform color naming (Mogg & Bradley,

1998a). Otherwise stated, emotional words arguably carry greater information load than

neutrally valenced words, thereby yielding higher reaction times.

One shortcoming of the Stroop is in interpreting the results; it is not clear whether

the response latency is due to interference by the word content or diversion of attention

from the word. This shortcoming of the Stroop precludes the ability to locate where

attentional biases occur over the course of information processing. In the absence of a

valid alternative, the Stroop remained the mainstay of attentional bias researchers for

over five decades.

Recognizing the significant limitations of the emotional Stroop task, MacLeod,

Matthews, and Tata (1986) developed an attractive alternative to the Stroop that removed

many of its shortcomings: The dot probe task. The dot probe task evaluates attentional

draining rather than interference to measure attentional bias. The basic task consists of

displaying a pair of emotional stimuli (words or images) simultaneously for a fixed









duration. A dot (probe) appears at the spatial location of one of the stimuli following

stimulus-offset. Participants are instructed to respond as quickly as possible to probe

onset by pressing a button. The task was developed based on the hypothesis that high

anxiety individuals oriented toward threat stimuli while low anxiety individuals divert

attention from the same. This hypothesis was supported by shorter response latencies to

dot probes appearing in place of the threat stimuli for the high anxiety group, and neutral

stimuli in the low anxiety group.

The dot probe has been used to uncover bias in various disorders, including eating

disorders, drug addiction, smoking, and trauma to name just a few by presenting cues

related to the respective disorders to patients suffering from those. The task was the first

to explain attentional bias without the confounding effects of interference, and has been

very influential in the formulation of the model of attention by Williams et al. (1987)

mentioned above. Further, the task presented a much clearer picture of the relationship

between trait anxiety and attentional bias, though lacking clear explanations of different

roles of state and trait anxiety.

The NN model of the classic Stroop task by Cohen et al. (1990) marked the first

model of an attentional task using NN. With this simulation, they were able to replicate

the major findings of the Stroop task better than any other existing model. Up until that

time, interpreting Stroop results was marred by its inherent shortcomings As a result all

explanations of the results were open to discussion and debate. The model explained the

results on the basis of the training utilized to get the network to produce the desired

results, using a concept called \il eugil ofprocessing (SOP). SOP refers to higher

activation levels for the units for particular inputs, which occurred due either of two









reasons; (1) an increase in strength of connections between the processing units, and (2),

higher resting activation levels of some input units. In other words, observed interference

was explained building on the mechanisms used to produce the same interference in the

network.

Essentially, the model put forward three different possible mechanisms of

attentional bias which the authors refer to as (1) exposure (involving repeated exposure to

the stimuli), (2) intensity (involving superactivating certain input nodes) and (3)

attentional (involving implementing a specialized unit that simulated monitoring for

threat and therefore influenced the activation levels of the other units) mechanisms. The

structure of the network consisted of two distinct pathways for the two tasks (explained in

greater detail in Chapter 2). As such, it eliminated the possibility of ascribing Stroop

effects to response interference, thereby providing a direct insight into the mechanisms

without the confounds that mar interpreting results of the Stroop task.

Matthews and Harley (1994) attempted to replicate the success of the Cohen model

by building a model of the emotional Stroop task. There were two main differences

between their model and that of the classic Stroop (Cohen et al., 1990); firstly, the Cohen

model simulated the time course of the psychological process (Cohen et al. derived a

relationship between the number of repetitions required to compute the output and the RT

typical for the condition being simulated, and then presented results in terms of the

computed RT) while the Matthews and Harley model did not. The second difference was

that Matthews and his Harley sought to investigate specific mechanisms that had emerged

from the first simulation rather than build the simulation to let the relationships emerge.

However, the authors later acknowledged that choosing not to simulate the time course in









the model limited its effectiveness. Still, the model was able to successfully simulate

Stroop interference for each mechanism.

Despite its vast applications and popularity in studies of attentive disorders, no such

model of the dot probe was developed until the current study. Although the dot probe has

been used extensively to study attentional bias, it remains a method primarily to

investigate the causes of bias and not the mechanisms that underlie these biases.

Although the collective empirical results are relatively coherent and consistent,

conflicting results have emerged. For example, some studies of social anxiety have

uncovered a bias towards socially threatening stimuli while others have not, leaving

confusion about the mechanisms of this particular bias. Our hope is that modeling the dot

probe task will yield potential answers to the questions while generating definite

considerations for future research in this area.

1.4 Limitations

Studies with the dot probe have yielded a vast database on various aspects of

attentional biases. However, conclusions regarding the underlying mechanisms that drive

these biases have been inferred from the data rather than directly investigated using

models. As a result, although research with the dot probe paradigm has yielded robust

relationships between the variables that comprise the task, these relationships have not

been clearly quantified for any of the samples tested. Consider the relatively well-

established relationship between trait anxiety, and valence and arousal level of the stimuli

used in the dot probe task. Specifically, individuals with high levels of trait anxiety react

faster to probes replacing the negatively valenced stimuli. However, the specific values of

trait anxiety, picture valence and arousal rating are unknown. These and other variables

of the dot probe task (e.g., stimulus duration, probe type, etc) cannot be easily quantified









by variations in task methodology, but potential answers can be generated by

manipulating the variables of the task in a computer simulation.

1.5 Statement of Problem

Prior to the current study, research to study the mechanisms of attentional bias

largely stemmed from studies of causes of attentional biases using paradigms such as the

dot probe task. Little work had been done to directly investigate the mechanisms by

developing models that mimicked human behavior when performing the dot probe task.

Although studies using different modifications of the dot probe and similar paradigms

yielded a huge amount of data, and significantly advanced understanding of attentional

bias, a model was needed that could be updated and verified (or challenged) on the basis

of new data. Further, although empirical work in this area is substantial, only a limited

amount of data is collected from these studies, thereby constraining the analyses that can

be performed.

1.6 Statement of Purpose

The purpose of this study was twofold; first, I constructed a NN model to simulate

performance on the dot probe task so as to investigate the underlying mechanisms of the

task. Second, a probabilistic model of the paradigm was constructed using Bayesian

networks to develop probabilistic relationships between the variables of the model. The

Bayesian model could also be viewed as a causal model and used to investigate the causal

impact of one variable on the others.

1.7 Current Study

No models had been developed to simulate human performance on the dot probe

task despite the multitude of studies performed to investigate the causes of attentional

bias using variations of the task. As such, the purpose of the investigation was to model









the dot probe task and its findings using a NN. The study further developed a

probabilistic model (i.e., a BN) to define discrete probabilistic relationships between the

variables of the task.

1.7.1 Objectives of the Neural Network Model

Multiple simulations with the NN model will be performed to investigate issues

related to the dot probe similar to the earlier works using the Stroop task (Cohen et al

1990; Matthews & Harley, 1994).

Matthews and Harley (1996) investigated three potential causal mechanisms of

attentional bias: exposure, intensity and threat monitoring (explained above). Simulations

in the current study investigated the first two of those causes vis-a-vis the dot probe task

and an additional mechanism consistent with the interaction hypothesis. Consistent with

the hypotheses of Matthews and Harley, the current study proposed that repeated

exposure to threat stimuli lead to an attentional bias towards such stimuli for the exposure

condition. The intensity mechanism posited that individuals assigned a higher negative

valence to a stimulus owing to higher levels of trait and state anxiety. The simulation

attempted to model this mechanism in a NN. Simulation 1 was identical to the preceding

simulation except that results will be presented in terms of RT rather than activation

levels and error of the network. In doing so, I hoped to overcome a significant limitation

of the Matthews and Harley model. Specifically, they did not simulate the timecourse of

psychological process. As such, the current study represents the first work to attempt to

do so. The first simulation was aimed at replicating the main empirical findings of the dot

probe task for each of the three mechanisms. Results were to be presented in terms of RT

in ms computed from equations derived from the number of iterations required to

produce the output, and the typical RT for the condition. The main assumption in this









case was that a linear relationship exists between the number of iterations required to

produce the output and the typical RT specific to each condition. As such, we made a

similar assumption to that of Cohen et al. (1990).

1.7.2 Objectives of the Bayesian Network Model

The Bayesian network (BN) model served as a "proof of concept" of the

advantages of probabilistic modeling in analyzing data. The Bayesian model of the dot

probe consisted of the following variables:

1. Anxiety level of the individual, entered as normalized scores on the STAI.

2. The arousal rating of the negative stimulus. This parameter reflected the arousal
value of the emotional stimulus presented to the individual. After the parameters
were set, the arousal value was computed using the probabilistic relationships
established for different values of the other variables.

3. The side on which the dotprobe appeared, specified simply as "same" or
"opposite" for dots replacing the negative and neutral stimuli, respectively.

4. The direction of attention, specified as either toward the negative stimulus or away
from it.

5. The reaction time, classified as fast and slow.

The model was used to perform inference, that is, find the probabilities of one or

more of the variables being in a given state, given the knowledge of the states of all or

some of the remaining variables.

1.8 Hypotheses

A hypothesis was associated with each of the two models to be developed in the

study:

Empirical findings from existing of the dot probe studies can be simulated using a
NN. Furthermore, a relationship does exist between the number of iterations
required by the network to compute the output and the RT for the particular
condition of the dot probe task. Finally, the NN will be able to correctly simulate
the various mechanisms of attentional bias.






13


6. Quantifiable and discrete probabilistic relationships exist among the variables in
the dot probe task that can be uncovered in the BN model.














CHAPTER 2
REVIEW OF LITERATURE

According to information on the website of the Anxiety Disorder Association of

America (ADAA [ADAA, 2004]), anxiety disorders (Generalized Anxiety Disorder

(GAD), Posttraumatic Stress Disorder (PTSD), Panic Disorder, Obsessive Compulsive

Disorder (OCD), Social Anxiety Disorder (SAD), and specific phobia affects) are the

most common mental illnesses in the United States, affecting 19.1 million adults (ages

18-54). Treatment of these disorders costs the U.S. more than $42 billion annually, twice

the amount spent on treatments for non-anxiety related disorders, including physical

illnesses (Simon, Ormel, Von Korff, & Barlow, 1995). Indeed, prescription drugs for

treatment of these illnesses are among the most commonly used in the world (Barlow,

2000). Of the various anxiety disorders, GAD, SAD and specific phobia affects together

afflict about 15.3 million individuals, or 10.9% of adult Americans. Further, GAD and

phobia affects are twice as likely to afflict women than men. People suffering from some

form of anxiety disorder are six times more likely to be hospitalized for a psychiatric

treatment than non-sufferers. Clearly, an understanding of the causes and mechanisms of

how anxiety can lead to anxiety disorders is required so as to devise better treatment

protocols.

For ages, philosophers have linked anxiety to the very essence of being human (see

Barlow, 2000), which is quite an ironic observation given that humans spend billions of

dollars every year to rid themselves of the same. Anxiety and anxiety disorders have been









observed in various cultures, from the Eskimo hunters of Greenland in the early part of

the last century, who experienced a sudden and extreme panic attack on their hunting

trips (Danish travelers to the region recorded it as "kayak aiig\ "') and not be able to

venture far out of the village again to a "sore neck" that affected the Khymer refugees in

more recent times. Another consistency of these disorders is their prevalence among

women. According to a WHO report, the odds of women being affected by some form of

anxiety disorders are 1.63 (95% confidence interval) (Barlow, 2000).

The aim of the current study is to develop a Neural network (NN) and Bayesian

network (BN) model of the dot probe task to investigate the underlying mechanisms. This

chapter provides a review of literature related to attention, attentional biases, and PDP

models developed to investigate the mechanisms of attention. The chapter reviews the

two PDP models of an attention task developed so far, specifically a model of the classic

Stroop task (Cohen, Dunbar, & McClelland, 1990) and a model of investigating the

mechanisms of the emotional Stroop task (Matthews & Harley, 1996). Literature related

to the dot probe paradigm is covered in significant detail to highlight methodology,

variables, and salient characteristics of the task.

2.1 Anxiety

Humans have a limited attentional capacity; implying that in order to efficiently

perform multiple tasks simultaneously, it is crucial to identify the task relevant cues and

the level of detail to which each cue must be processed. The information processing

system then must process these relevant cues in requisite detail and ignore the others; a

job delegated to the attentional system As a result, the system plays a key role in survival

1 Panic attack experienced by Eskimo seal-hunters while hunting alone for days in their kayak. After the
attack, the afflicted hunter could not venture but a few miles out of the village.









and evolution (Mogg & Bradley, 1998a). However, the amount of attentional capacity

available is affected by the emotional state of the person.

Research over the last two decades has led to several robust findings linking

anxiety to performance decrement on a broad range of tasks. Woodman and Hardy (2001)

refer to anxiety being generally accepted to be an unpleasant emotion. Lang (2000)

describes human emotions to have developed around two key motivational systems that

play key roles in evolution and survival, namely the appetitive and defensive systems.

Emotions in general and anxiety in particular influence the selective attention and

information processing capability of an individual. The general propensity of an

individual to experience high anxiety and the short-term anxiety he or she experiences in

a particular situation are distinguished as trait anxiety and state anxiety respectively.

However, trait anxiety does have a bearing on the level of state anxiety experienced by an

individual; typically, individuals with trait anxiety have a tendency to experience higher

levels of trait anxiety in stressful situations when compared to low trait anxious

individuals (Williams, Watts, MacLeod & Matthews, 1988).

2.1.1 Measuring Anxiety

Anxiety is mainly measured through paper-and-pencil self-report questionnaires. One of

the most frequently used scales to measure levels of state and trait anxiety is the

Spielberger's State and Trait Anxiety Inventory (STAI) (Spielberger, Gorsuch., &

Lushene, 1970). The STAI has both a state version (STAI-S) and a trait version (STAI-

T); the state version is the most commonly used inventory to measure state anxiety. Both

versions consist of 20 questions; the STAI-T consists requires individuals to rate how

they generally feel on a 4-point frequency scale (from 1 = almost never to 4 = almost

always) while its state counterpart asks them to rate their feelings at that moment on a 4-









point intensity scale (from 1= not at all to 4 = very much so). Maximum possible score on

both versions is 40 while the minimum possible is 10. The test has been reported to have

high internal consistency (Spielberger, Gorsuch, Lushene, Vagg, & Jacobs, 1983).

Other popular inventories include the Autonomic Perception Questionnairre

(APQ) (Mandler, Mandler & Urviller, 1958), the Affective Adjective Checklist (AACL)

(Zuckerman, 1960), and the Activation-De-activation Checklist (AD-CL) (Thayer, 1967).

One drawback common to all self-report methods is the inability of the participants to

accurately and reliably report on their cognitive processes (Nisbett & Wilson, 1977).

2.1.2 Cognitive Models of Anxiety

A number of cognitive models of attention and attentional biases have been put

forward to explain the relationship between anxiety and attention. One key feature

emerging from these models is that attentional bias is critical in the origin and

maintenance of anxiety and emotional disorders like GAD. Up until the latter part of the

1980's, there were two main theories explaining how anxiety affects attention, Beck's

cognitive theories of emotional disorders (Beck, 1976; Beck, Rush, Shaw, & Emery,

1979; Beck, Emery & Greenberg, 1986) and Bower's theories based on his network

model (1981). Beck's theories, in particular, have been influential in devising new

treatment protocols for depression and anxiety, specifically cognitive-behavioral therapy

(Butler, Fennell, Robson, & Gelder, 1991; Simons, Murphy, Levine & Wetzel, 1986).

Beck (1976) proposed that humans have set schema that they use to process the

information. All incoming information passes through the schema, which attaches

semantic meaning to it. In people suffering from anxiety disorders, the schemata

pertaining to processing threat or danger are dysfunctional, resulting in selective









processing of schema-congruent information when activated. Similarly, depression is

associated with dysfunctional schemata related to loss or failure.

Bower (1981) explained the same phenomenon using an associative network of

emotions and memories of events. In such a network, emotions are connected to

memories of relevant events (happy and sad) to form nodes of the network. Activation

can travel in either direction; activating a particular emotion node can trigger specific

memories and vice versa. When activated, a node also activates, to some extent, the

nodes connected to it. For instance, normally the node representing "sadness" is linked to

nodes representing memories of sad events. Feeling "sad" will trigger memories of sad

events and thinking of these events will activate sorrow. This means that events are

tagged with their emotional value before being stored in the network. In depression,

events are tagged as negative more frequently and as having higher intensity of

negativity. This increase in strength of connection between the memory nodes and the

incoming information nodes implies that even events with low values of sadness have a

higher negative impact on depressed individuals, as compared to normal individuals and

also strengthen the connections more. Similarly, attentional bias towards anxiety causes a

tendency towards selective processing of negative or threatening information, causing the

individual to experience higher levels of anxiety.

Both models explain the role of anxiety in causing and maintaining attentional

biases. Overwhelming evidence exists in support of most of the predictions of both the

above models (e.g., Clark & Teasdale, 1982; Bradley & Matthews, 1983; MacLeod et al.,

1986). However, the models fail to explain some of the findings emerging from the

studies on attentional biases. In particular, both models predict that both anxiety and










depression should be associated with attentional biases on all aspects on information

processing, namely selective attention, reasoning, and memory (Mogg & Bradley,

1998a). However, studies have failed to uncover any evidence either of an attentional

bias towards threatening stimuli in depression (MacLeod et al., 1986) or of a recall

(memory) bias in anxiety (Mogg, Matthews & Weinman, 1987). On the contrary,

research suggests anxiety is linked to an attentional bias towards threat while depression

is associated with a memory bias towards negative information (Mogg & Bradley,

1998a).



"State x Trait interaction" view (Williams, Watts, MacLeod, & Matthews,

Resource Allocation Mechanism
Hig High trait anxiety: orient towards location of threat
High 71
Stimulus Affective Threat
Stimulus Affective Threat Low trait anxiety: shift attention away from threat.
input Decision
Mechanism


No
Threat
State Anxiety Threat Trait anxiety determines whether
(mimics effect of processing resources are directed
high threat input) towards or away from a stimulus that
has been judged to be threatening


Figure 2.1 Cognitive mechanisms underlying biases in initial orienting to threat in
anxiety

To explain these findings, Williams et al. (1988) proposed a new model relating

attentional biases to anxiety and depression. To begin with, they associated anxiety with a

tendency for preattentive vigilance for threat and depression with a bias towards

postattentive elaborative processes, thereby explaining the lack of a recall bias is anxiety

and a similar lack of bias in preattentive processes in depression. The model proposes

two mechanisms for directing preattentive and attentional bias towards threat stimuli in









high anxiety individuals; the Affective Decision Mechanism (ADM) evaluates the threat

value of incoming stimuli and outputs the result into the Resource Allocation Mechanism

(RAM) (Figure 2-1). The RAM allocates attentional resources towards or away from

threat based on trait anxiety of the individual with high trait anxious individuals having a

tendency to orient towards threat and low trait anxious people orienting away from the

same; this is the interaction hypothesis. As indicated in Figure 2.1, the difference between

high and low anxious individuals becomes more pronounced with an increase in the

threat-value attached to the stimulus by the ADM. Consequently, the ADM can be

thought of as a mechanism to assign priorities to incoming stimuli. Three main themes of

the model are:

1. Anxiety is associated with different patterns of selective attention rather than with
detailed information processing. Cognitive bias for anxiety acts on the preattentive
stage, looking for threatening stimuli in the environment.

2. Individuals who have a tendency to display an attentional bias towards threatening
stimuli are more prone to anxiety and anxiety disorders under stress.

3. Trait anxiety influences the direction of the attentional bias, implying individuals
with high trait anxiety are more likely to experience a higher level of state anxiety
in more situations.

Williams, Watts, MacLeod and Matthews (1997) revised their 1988 model within

a connectionist framework Parallel Distributed Processing model of Cohen et al. (1990).

The revised model is explained following the review of PDP models of the Stroop task

below.

Recent theories of anxiety appear to complement the Williams et al. (1988)

model. For example, Matthews (1990) proposed that emotions serve to assign processing

priorities to incoming stimuli based on the view of evolutionary functions of emotion

(Oatley & Johnson-Laird, 1987). Eysenck (1992) devised the hypervigilance theory on









the basis of the interaction hypothesis. He proposed that not only are high trait anxious

people more biased towards attending to threat information (i.e., high specific

hypervigilance) but they may attend to any task irrelevant stimuli when anxious (i.e., high

general hypervigilance or distractibility). The theory further suggests that high trait

anxiety results in a higher rate of environmental scanning, with the general focus of

attention being very broad but becoming narrow when focusing on cue relevant stimuli.

Eysenck and Calvo (1992) explained the effect of anxiety on selective attention

and subsequently on performance with the Processing Efficiency Theory (PET).

According to the theory, processing of anxiety-relevant stimuli increase demands on

working memory, thereby reducing the amount of resources available to process task

relevant information. Another possibility emerging from the PET is that performance

decrement exhibited by high trait anxious individuals on experimental tasks in

individuals occurs because they selectively attend to stimuli that are relevant to their

anxiety and not to the task at hand.

The PET is a formalization of the line of cognitive research being followed in the

study of anxiety. Research emphasis has been to focus on the patterns of allocation of

selective attention to tasks associated with high anxiety (Matthews & McLeod, 1994).

The susceptibility of high anxious individuals to attentional bias towards processing

information relevant to their anxiety is a robust finding and has been repeated in various

situations with a host of different populations.

The role of attentional bias in selective attention has been explained using a

searchlight analogy (Williams et al., 1997): Selective attention is likened to a searchlight

beam, with the area illuminated by the beam as the center of attention. Some peripheral









attention is devoted to information in the area not illuminated directly by the searchlight.

This information can cause an involuntary shift in attention causing attentional draining

from the main task and thereby leading to deterioration in performance. Attentional bias

is explained as an attentional vigilance to threat and has been projected as the main factor

in causing and maintaining anxiety (Matthews, 1990; Eysenck, 1992). Bradley, Mogg,

Falla, & Hamilton (1998, p. 737) explain this cycle: "Individuals with a tendency to

adopt such a vigilant attentional style would be more likely to detect potential sources of

danger in their environment, which in turn would exacerbate their anxious mood."

Ohman (1993; Ohman & Soares, 1993, 1994) reached similar conclusions from a

different research perspective. They suggested that preattentive processes also regulate

vulnerability to phobias with fear evoking stimuli working in much the same way as

threat stimuli in anxiety. Specifically, fear responses to stimuli are initiated by automatic

analysis mechanisms. These mechanisms are guided by biologically prepared threat

stimuli and direct attention to the stimulus once it is analyzed.

2.2 Attentional Bias

The above discussion reveals the importance of attentional bias in evaluating

incoming stimuli and directing attention. Williams et al. (1997) assume an attentional

bias to have occurred when there is a discrete shift in attention to some change in the

environment of the individual. They specify three assumptions regarding the shift in

attention resulting from the bias essential in studying attentional biases:

4. The shift encompasses all sense modalities (vision, touch, taste, smell, etc)

5. Although usually passive and involuntary, the shift can be voluntary (i.e., attention
can be deliberately focused on the area).

6. Onset of the shift is brought about by a discrete change in the environment (i.e. by
the onset or offset of some event).









Researchers have used two basic paradigms to study attentional biases, interference

methodologies (specifically, the dichotic listening paradigm and its visual analog, the

Stroop task), and methods to test directly for attentional bias (namely, the visual search

and dot probe paradigms).

2.2.1 Dichotic Listening Paradigm

Mainly used in studying selective attention, the dichotic listening paradigm and its

visual analog are now the least preferred paradigms for studying attentional biases. The

basic version of the task consists of simultaneously playing a different audio message in

the left and right ear of the subject using headphones. Participants are then asked to

"shadow" (say out aloud) one of the messages as it is played. Early studies found

participants could effectively follow only one of the messages, though some information

(e.g. a high pitch tone, or change from a male to female voice) from the unshadowed

message still got through. The explanation offered was that the messages were

distinguished on the basis of some physical characteristics (e.g., pitch, amplitude, etc.).

For a full review of theories of selective attention see (Abernethy, 2001). The paradigm

was instrumental in establishing that attentional bias acts early in the information

processing system.

In the study of attentional bias using dichotic listening paradigm, the task was

based on the premise that anxious individuals were more likely to attend to threat and

other stimuli that directly related to their life events. Parkinson and Rachman (1981) used

the task to study lowered auditory thresholds in concerned mothers. They presented audio

messages consisting of words representing pain and other unpleasant stimuli embedded at

various volumes to two groups of mothers; those whom had children admitted to the

hospital for some surgical procedure and a control group with no children admitted.









Results indicated the experimental group identified more embedded words than the

control group.

The paradigm lost stature following a study on PTSD sufferers (Trandel &

McNally, 1987), in which it failed to find any attentional bias in war veterans towards

Vietnam-related words. Participants with and without PTSD experienced similar

disruptions to all threatening stimuli; this was a major shortcoming since it does not allow

the method to be made reliably sensitive to the specific fears of the population being

studied.

2.2.2 Stroop Task

The classic Stroop task (Stroop, 1935) consists of displaying names of colors

written in different colored inks (Figure 2.2(a)) in which participants are required to

either read the word or name the color of the ink as quickly as possible. The dependent

measure in this case is the response time to name the color or read the word. Typically,

participants are able to ignore the effects of ink color while reading the word aloud but

experience significant interference with the word when trying to name the color of the

ink. Interference is greatest if the word is an antagonistic color-name (e.g., word

"GREEN" printed in red ink (Figure 2.2(a)) or represents an antagonistic color (e.g. word

"GRASS" printed in redink) (Jensen and Rohwer, 1966, MacLeod, 1991). Meaningless

stimuli (e.g., a row of X's) do not interfere with the ink naming at all while congruent

colors slightly facilitate naming the color ("RED" printed in red ink [Figure 2.2(b)]).

Various explanations have been presented for the observed discrepancy in

response times for color-naming and word-reading. The simplest one explained the

observed interference on the basis of discrepancy in processing times required for the

word reading and color naming. Researchers proposed that color naming is more









automatic than word reading and so takes longer to process than word reading, causing

interference at the output level. So, although both inputs were detected simultaneously,

response from word reading arrived at the output level before its counterpart from the

color-naming task. However, Glaser and Glaser (1982) put the explanation to test and






GREEN RED SPIDER



a. Conflict b. Congruent c. Emotional Stroop
condition, GREEN condition, GREEN in for spider phobics,
in red ink red ink in red ink


Figure 2.2 Versions of the Stroop task.

proved it inadequate; they provided participants with advanced knowledge of the ink

color by displaying a color patch of the same color as the color of the ink. Participants

displayed interference effects even when the color patch was displayed 400 ms before the

word. The effects came to be known as Stimulus Onset Asynchrony (SOA) effects.

A more robust explanation was offered by MacLeod and Dunbar (1988) on the

basis of degree of automaticity of different tasks. Numerous studies have established that

automaticity on a task increases by practice according to the power law (Kolers, 1976;

Newell & Rosenbloom, 1981; Anderson, 1982; Logan, 1988). MacLeod and Dunbar

(1988) reasoned that if amount of practice could make a task more automatic, it would

show up in appropriate changes in Stroop interference with the more automatic task

interfering with the performance on the less automatic one. To test the hypothesis, they

trained individuals to associate four different shapes with four different colors.









Participants were trained by presenting the shape in a neutral color (white) with each

shape being presented 72 times. The same pattern of training was carried out daily for 20

days. At the end of the first day of training, participants were administered the Stroop

task with the shape. On an average, participants were 100 ms slower at shape naming

than at naming colors. The end of the fifth day saw significant increases in speed of shape

naming, with the shapes interfering with color naming. By the time the study was

completed (20 days of 72 trials per stimulus for a total of 2,520 trials per stimulus),

participants displayed significant interference with color naming and a small amount of

facilitation in naming colors (evident from increased RT when the shape and color were

conflicting and reduced RT when the shape and the color were congruent). On the other

hand, colors showed very little effect on shape naming (shapes had taken the place of

words and become the more automatic task).

Word reading is considered an automatic task because individuals have arguably

practiced it more than the more controlled and less practiced task of color naming. The

theory has since been modified based on the findings of MacLeod and Dunbar (1988),

who proposed that tasks have varying degrees of automaticity and control. Specifically,

the degree of automaticity of tasks is a continuum rather than a dichotomy (i.e., tasks are

not simply controlled and automatic but vary in their degree of automaticity or control,

with some being more automatic than others). For instance, if a study consists of two

tasks with one being more automatic than the other, performance on the less automatic

task will suffer due to interference from the more automatic process.

The emotional version of the Stroop task used a negative affective word instead of

a color name. Participants had to name the color of the negative word (words









representing specific phobias for phobics). Figure 2.2(c) depicts a slide presented to a

spider phobic. The emotional Stroop is an adaptation of the classic Stroop task that

compares the response times of participants on color naming a series of emotional words

as opposed to color-names (Matthews & Harley, 1996; Williams, Matthews & MacLeod,

1996). For anxiety, the affective word is either threatening (e.g. "death", "injury",

"sickness") or non-threatening word (e.g. "chair", "picture"). Individuals with high trait

anxiety were hypothesized to display higher levels of interference in naming the ink color

of a threatening word rather than a non-threatening word. Studies have found results

congruent with the hypothesis.

The first study using this paradigm was conducted on patients suffering from

GAD (Matthews & MacLeod, 1985). They found the experimental group to be

significantly slower at naming the color of threat words. Similar results have since been

observed in patients suffering from a host of different emotional and anxiety disorders,

including Post traumatic stress disorder (PTSD) (Threasher, Dalgleish & Yule, 1994),

obsessive compulsive disorder (OCD) (Lavy, van Oppen & van den Hout, 1994), specific

phobics (IAS, like social and spider phobics) (Lavy, van den Hout & Arntz, 1993) and

panic disorders (McNally, Amir, Louro, Lukach, Reimann & Calamari, 1994). One key

finding apparent from studies with population groups suffering from different anxiety and

emotional disorders was that individuals with these disorders exhibit the greatest

difference in interference with the corresponding control groups when the valence words

used represent threats relevant to their specific condition. For example, in a study with

GAD patients worried about physical injury, Mogg, Matthews & Weinman (1989) found

that participants displayed the most interference when the word was related to physical









danger (e.g. injury, fracture, etc.). Similarly, the greatest interference effects for social

phobics are induced by words representing socially threatening situations (Hope, Rapee,

Heimberg, & Dombeck, 1990), and words of physical threat cause the greatest influence

for panic disorder patients (McNally, Amir, Louro, Lukach, Reimann, & Calamari ,

1994).

Researchers put forward different explanations to account for the findings

associated with the emotional Stroop task. One view was that anxious individuals allocate

more attentional resources to threat words and process them in greater detail due to an

attentional bias toward threat. The increase in resources consumed by processing threat

information lead to the interference. A second explanation posits that threat words cause

a spike in the level of state anxiety, disrupting performance on color-naming task. Some

researchers (MacLeod, 1990; de Ruiter & Brosschot, 1994) questioned the validity of

both the above explanations, stating that a tendency to divert attention from emotional

cues can also lead to observed interference. The latter explanation was only the first of

several criticisms levied against the emotional Stroop task.

One major drawback of the emotional Stroop variations was in interpreting the

results of the task; the task offered no evidence as to whether the interference occurred at

the information processing stage or at the response selection stage. Further, it failed to

shed any light on the role of state and trait anxiety in the observed effects. Interpretative

difficulties apart, the paradigm also lead to some unexpected results. Specifically, studies

with phobics did not find any threat-related interference when participants were in close

proximity (physical or chronological) with their threat situation or object. For example,

snake phobics in the presence of snakes (Matthews & Sebastian, 1993) and social phobics









getting ready to give a speech right after testing (Amir, McNally, Reimann, & Clements,

1996) did not reveal expected interference effects for snake and threatening social

situation related words. Finally, the task measured only deterioration in performance due

to attentional bias (Willams, et al., 1997). However, interpretative difficulties remain, by

far, the more serious shortcoming of the task.

2.2.3 Dot Probe Task

Interference paradigms like the dichotic listening paradigm and the Stroop task

failed to offer a direct indices of the mechanisms underlying attentional bias, as explained

by the interpretative difficulties encountered in the Stroop task. Alternatives to these

tasks are the visual search paradigm and the dot probe paradigm. The dot probe is a direct

measure of attentional bias experienced by individuals (Williams, et al., 1997).

Developed by MacLeod, Matthews and Tata (1986), it was modified from paradigms in

cognitive psychology that used response time to visual probes to assess attention

(Posner, Snyder & Davidson, 1980; Navon & Margalit, 1983). These paradigms

suggested that participants would respond faster to a probe stimulus when it appeared in

an attended rather than unattended region of visual attention.

The paradigm measures attentional drain due to existing biases in attention without

confounds of response selection by measuring the reaction time of a neutral response

(button click) to a neutral stimulus (dot-probe). The basic steps (Figure 2.3) consist of

simultaneously displaying an emotional cue (word or picture) paired with a neutral cue

for a short duration of time (traditionally 500 ms though other times have been used).

Following cue offset, a dot appears in the spatial location of one of the two cues.

Participants are instructed either to indicate the position of the probe (probe position task,

i.e., indicate whether the probe appears on the left or right, or top or bottom by pressing










the appropriate button) or indicate its type (probe classification task; two different probes

are used, say the letters 'E' and 'F', and participants are required to indicate the letter) as

quickly as possible. The driving hypothesis for the MacLeod task (another name for the

dot probe used in literature) was that high anxiety individuals systematically attend to

threat-related stimuli and this would be reflected by faster response times to probes

replacing emotional cues as opposed to non-threatening cues and also response times of

non-anxious individuals for the same cues.

2.2.3.1 Initial studies (basic dot probe task)

The first dot probe study (MacLeod, et al., 1986) used the paradigm to measure

attentional bias in GAD patients. Sixteen individuals diagnosed with GAD and referred

for anxiety management by their practitioner were tested against a group of sixteen low

anxiety (LA) controls. The GAD group obtained mean scores of 44.7 and 52.5 on the





3. Dot probe appears in the
spatial location occupied by one
S* of the stimuli immediately
following the offset of the
stimuli.
CHAIR
2. Stimuli appear (arranged
DCHAIR BLEED either vertically or horizontally)
BLEED


-+ 1. Fixation cross appears for a
fixed duration (typically 500 ms)

time

Figure 2.3 Illustration of the dot probe paradigm

state and trait versions of the STAI while the LA group scored 36.3 and 39.5,

respectively. On the Beck Depression Index (BDI), GAD sufferers and controls groups









scored 13.9 and 7.6, respectively, with GAD patients being significantly more depressed

than their LA counterparts (the significant difference in the depression levels of the two

groups added a confound that was later removed by testing a low-anxious depressed

sample against controls). Patients were matched with controls for age, gender and verbal

intelligence (measured by the Mill Hill Synonyms Test). Each group was shown a total of

288 word-pairs on a computer monitor; 48 consisted of a threat word paired with a

neutral word while the remaining 240 were a pair of neutral words. Of the threat words,

half represented physical threat while the other half represented social-threat.

Words were displayed centered on the vertical axis of a VDU (Visual Display

Unit), separated by a distance of 3 cm from each other (constituting a visual angle of less

than 2 degrees), for 500 ms. Participants were instructed to read out loud the word

appearing on the top in every trial and to press a button as quickly as possible when a

probe appeared to indicate its presence. The probe (a white dot that appeared with equal

probability in the spatial location of one of the two words) appeared in 96 trials and

remained on the screen until participants pressed a button to indicate its presence. All

threat-neutral pairs (48 in all) were followed by the probe while the other 48 probed trials

consisted of filler items chosen at random from the neutral pairs. Trials could thus be

classified into three types; probed-threat, probed-neutral, and unprobed-neutrals. On trials

without the probes, the next picture was displayed following a delay of one second.

Results confirmed the hypothesized preferential attention to threat information by

the GAD group and an avoidance of the same displayed by controls. When the probe

appeared at the top, the GAD group was significantly faster at responding when it

followed a threat word (593 ms) than a neutral word (652 ms). The same trend was









observed for probes appearing in the lower section of the screen, with the high anxiety

group responding faster when the probe was preceded by a threat word (663 ms) than

when it followed a neutral word (695 ms). Reaction times for the control group followed

the reverse trend, with controls reacting faster to probes replacing neutral words than

threat words, implying an avoidance of threat cues. Specifically, controls recorded

reaction times of 540 ms when the probe replaced a threat word in the upper area vs. 524

ms when it replaced a neutral word in the same location; for probes appearing in the

lower area of the display, controls were 32 ms faster in responding to probes following

neutral words (584 ms) as compared to threat words (616 ms).

The study was among the first to offer an explanation for attentional bias towards

threat stimuli without any confound from response bias (as would have been the case if

Stroop task had been used) of the results. Results from this and other dot probe studies

were critical in formulation of important assumptions regarding the nature of attentional

bias. Williams et al. (1997) acknowledged the contribution of the paradigm as,

It [the MacLeod et al. (1986) study] showed that we needed to assume the existence
of a decision mechanism which (a) was at a preattentive level, (b) was sensitive to
general differences in threat, (c) allocated attention to different parts or aspects of
the environment, and (d) was independent of response bias (Williams, et al. 1997,
p. 83)

In a subsequent study using the paradigm, Broadbent and Broadbent (1988)

attempted to answer some of the questions emerging from MacLeod et al. (1986). They

investigated whether preferential allocation of attention to threat stimuli was a

characteristic of only clinically anxious people or if people with sub clinical levels of

anxiety also display a similar bias. Further, they questioned whether the effects were a

function of the personality of the individual (and therefore permanent) or more a function









of the state of the individual regardless of personality characteristics (and so more

fleeting).

Making a few minor changes to the setup of MacLeod et al. (1986), they tested a

total of 104 women in four different experimental setups to answer the above questions.

In each experiment, they divided the women into a HA group and a LA group based on

their STAI scores. Individuals scoring greater than 35 on the trait form of the STAI were

classified as HA while those scoring less than that were classified as LA.

Results confirmed the existence of a similar bias in the sub-anxious sample and an

avoidance of threat information by the LA group. On the whole, HA participants

responded faster when probes appeared in place of threat stimuli as opposed to when the

probe replaced the neutral stimulus in the threat-neutral pair while the reverse was true

for LA participants. When threat words appeared in the upper area, HA individuals

responded faster to probes replacing the threat word (587 ms) than to probes that replaced

the neutral word in the threat-neutral pair (637 ms). Similarly, when the probe and the

threat word, both appeared on the bottom, the HA group took 650 ms to press the button

while taking 667 ms when the word appeared on the bottom and the probe appeared on

top. Opposite readings were observed for the LA group; individuals were slower to

respond to probe appearing in the location of the threat word (RT 656 ms and 678 ms for

probes and threat words on the top and bottom, respectively), while reacting faster to

probes that replaced the neutral word in the threat-neutral pair (649 ms for threat word in

upper position and probe in lower and 657 ms for the opposite). They also found trait

anxiety a more reliable indicator of attentional biases as compared to state anxiety; high

trait anxious participants in their study consistently displayed similar patterns of









attentional bias while the effect of state anxiety differed from one experiment to the

other.

Around the same time, MacLeod and Matthews (1988) ran a follow-up study to

investigate the effects of state and trait anxiety on attentional biases. They tested 36 high

and low trait anxious (non-clinical) college students for attentional biases towards exam

related cues under conditions of low stress (12 weeks before the exam) and under high

stress (one week before the exam). Here again the STAI (trait) score (dividing median

score 39.5) was used to stratify the students into high and low anxious categories.

Participants were presented 288 word pairs, 96 of which were probed. The probed pairs

consisted of an equal number of threat and neutral pairs. Half the threat words used in

this case were related to examinations while the other half were general threat words

chosen from earlier studies. Words were rated for threat value and pertinence to

examinations on a scale of 1-5 (1 being the least and 5 the maximum on both scales) by

eight independent judges and both groups of threat words had the same threat rating (4.1).

Authors computed the attentional bias score to analyze the results by subtracting

the mean RT when the probe occurs in the same place as the threat word from the mean

RT when the probe and the threat cue occur in different locations.

Attentional Bias (UP/LT UP/UT) + (LP / UT LP/LT)
Attentional Bias =
2

UP = Upper Probe, UT= Upper Threat

LP = Lower Probe, LT= Lower Threat

Positive values of bias score signified vigilance of threat and negative values

indicated avoidance of threat. Attentional bias scores were used to obtain a single index

of probe and threat positions so as to simplify computing a four-way interaction of trait









anxiety, test time, threat position and probe position. Results revealed a tendency to

attend to threat stimuli in general by the high trait anxious group and avoidance by the

low trait anxious group. Exam words did not attract much attention from either group in

the first test but did so in the second. Also both groups recorded equivalent increases in

state anxiety but with opposite effects. The HA group responded even faster when the

probe and threat appeared in the same location while the low anxious group recorded

shorter latencies to probes replacing the neutral word in critical pairs. This pattern of

change could not be explained on the basis of trait anxiety alone and lead the authors to

infer that the patterns were in fact due to an interaction of state and trait anxiety.

Researchers later referred to this pattern of attention allocation and the effect of state and

trait anxieties on it as the interaction hypothesis (Williams et al., 1988).

The dot probe has proved to be an effective measure of attention allocation and

preattentive bias to different kinds of stimuli. Studies have replicated the task and

confirmed the existence of similar patterns of attention allocation in several different

samples. Different studies effected changes in the task methodology, making the task

more sensitive to the sample being studied. One shortcoming with early versions of the

task was due to probing in only a portion of the trials. This limited the amount of data

that could be collected. Also, because each threat word was probed, the appearance of

such a pair could act to prime participants for the probe and hence result in a faster RT.

Mogg, Bradley and Williams (1995) disposed of this requirement by probing

participants at the end of every trial and instructing them to indicate the position of the

probe (top or bottom for cues displayed centered on the vertical axis) by pressing the

appropriate button. Trials on which the threat-word, neutral word pairs were displayed









came to be known as critical trials. Using this methodology also rendered the requirement

of reading aloud the top word infeasible, eliminating another confound. One potential

flaw of probing in every trial was the possibility of participants adopting a strategy to

attend to the spatial location of one word only (and press the button indicating presence

of the probe depending on whether the probe appeared on the side they were attending to

or not). MacLeod and Chong (1999) overcame this potential pitfall with the "forced

reaction time" version of the task. Essentially, they used two different probes (two dots in

vertical and horizontal orientation ':' and '..') and participants were instructed to perform

probe classification, pressing a different key depending on the type of probe used.

One criticism the basic dot probe shared with the Stroop was that it too provided

only a snapshot of attention at the instant of probe onset. Specifically, both tasks only

provide a definite answer of the direction of attention when the dot probe appeared, but

no information to the direction of attention allocation prior or subsequent to the probe.

Three explanations have been offered to account for the observations of the dot probe.

First is the vigilance-avoidance pattern of processing (Mogg, Matthews and Weinman,

1987; Williams et al., 1988), which says anxious individuals follow a pattern of first

attending to and then avoiding the threat cue in an effort to mitigate their anxious state.

Such a pattern may also act to maintain their anxiety-state by preventing anxious

individuals from habituating to threatening events. A second possibility, consistent with

the models of Beck (1976) and Bower (1981), is that anxious individuals orient

themselves toward threat and subsequently have trouble disengaging attention. To answer

these questions required modifying the task of MacLeod et al. to measure the time course

of attention.









2.2.3.2 Manipulation of stimulus duration

Mogg, Bradley, de Bono and Painter (1997) modified the task to measure attention

at three different times by manipulating stimulus duration. They presented 192 word pairs

(96 threat-neutral and 96 neutral-neutral pairs) to 35 volunteers in top-and-bottom

orientation, and displayed each word pair randomly for 100 ms, 500 ms or 1500 ms. The

first condition was designed to be shorter than the inter-saccadic interval during active

visual search (varies between 200-300 ms: Kowler, 1995) and therefore did not allow any

shifts in attention. On the other extreme, 1500 ms allowed for detailed processing of the

stimuli and multiple overt shifts in attention. The 500 ms condition represented the most

frequently employed time period for the dot probe. They also varied the inter-stimulus

period randomly among 750, 1000 and 1250 ms. Threat words consisted of an equal

number of words referring to social threats (e.g., stupid, despised, criticism) and physical

threat (e.g., illness, injury, fracture). Word-pairs in critical trials were ordered such that

there was an equal probability of the type of threat-word displayed (social, physical), its

location (top, bottom) and the probe position (top, bottom). Participants' emotional states

were assessed after they completed the task by having them fill out the STAI, BDI, and

Social Desirability Scale, among others, and were divided into two groups (high and low

state anxiety) based on their STAI-state scores (dividing median score 30) for analysis.

After removing outliers from the data (trials with high error rates and RT more than

three standard deviations from the mean), Mogg et al. (1997) they found a significant

main effect for exposure in that individuals tended to respond faster to probes in the 100

ms duration (485 ms) as opposed to the other two conditions latenciess of 498 ms and 503

ms for 500 ms and 1500 ms conditions) regardless of trait anxiety. High state anxious

individuals showed a significant trend to respond to threat, recording response times 10









ms faster to probes replacing threat words (mean 493 ms) than those replacing neutral

words (503 ms). On the other hand, low anxiety scorers displayed a non-significant effect

of threat-avoidance, with RT for threat words 8 ms slower than for neutral words (502 ms

and 494 ms, respectively). Bias scores for the high state anxiety group were 10, 9, and 11

and -11, -10 and -1 for the low state anxiety group for the 100, 500 and 1500 ms

conditions respectively. Post hoc analysis revealed significant difference in bias scores

averages over the three conditions for the two groups, with significant differences in the

100 ms condition and non-significant trends between the other two.

Findings did not support the vigilance-avoidance hypothesis, that is, there was no

significant difference of attentional bias with display duration. According to the

vigilance-avoidance hypothesis, dysphoric individuals have an initial attentional bias

towards threat cues, which puts them in an aggravated state of fear. In order to escape this

state, they direct attention away from the stimuli. The authors refrained from making any

generalizations on the basis of this study, as it was the first in the field, and offered two

explanations for the observations; first, they suggested that approach-avoidance could be

more likely a characteristic of individuals with anxiety disorders (GAD, panic disorder,

etc.) rather than those with sub clinical anxiety, and secondly, they suggested that

attentional avoidance could be influenced by the relative threat value of the stimulus.

2.2.3.3 Backward masking

Backward masking of stimuli was a technique used in the Stroop task to restrict

awareness and measure strictly preattentive bias towards threat cues. It involved

displaying the word for a very short time (e.g., 14 ms) and then replacing it with a length-

matched mask (random characters). The mask worked to prevent detailed processing of

the word and thus strictly measured pre-attentional bias. The same was adapted for the









dot probe. All word pairs were displayed for a very short duration (typically 14 ms), and

then covered by a mask (consisting of random letters or symbols, one for each letter of

the word, or contortions of the letters of the words themselves) for a similar duration. The

probe followed stimulus-offset and participants were required to perform probe position

orprobe classification task. The hypothesis for the masked dot probe remained virtually

unchanged from the basic version; HA individuals were predicted to attend to the spatial

location formerly occupied by the mask covering the threat word. Results of studies using

this version of the dot probe confirmed the hypothesis with HA individuals and those

with GAD (Bradley, Mogg & Lee, 1997b; Mogg et al., 1997).

A barrier in generalizing findings from the above studies and other dot probe

studies using single words as threat stimuli is the amount of threat information that single

words can convey. As noted by Bradley et al. (1997a) and Mogg et al. (1997), single

words convey a limited amount threat-information and, once that information is

extracted, the word loses part or all of its threat value. Additionally, a potential confound

exists due to the threat value and relative frequency of use of threat words as HA

individuals use threat words more often more than LA individuals. Finally, research

suggests that attentional biases are guided by innate, evolution-driven mechanisms;

words do not fulfill the criteria fit of ecologically valid threat stimuli (LeDoux, 1995). An

alternative to single words is using photographs of threat stimuli (mutilated bodies,

attacking animals, angry faces). Pictorial cues are a much more ecologically valid threat

cue than single threat words.

2.2.3.4 Pictorial dot probe task

Bradley and his colleagues (Bradley, Mogg, Millar, Bonham-Carter, Fergusson,

Jenkins, & Parr, 1997) designed a pictorial dot probe task, using pictures rather than









words as the emotional stimuli. They displayed pictures of faces with happy, threatening

or neutral expressions for 500 ms to a sample consisting of sub-clinical HA students

(grouped according to scores obtained in the upper and lower tertiles of the Fear of

Negative Evaluation scale (FNE; Watson & Friend, 1969)). On critical trials, an

emotional face was paired with a neutral face and participants were required to indicate

the position of the dot. Results did not indicate a relationship between social anxiety and

attentional bias but post-hoc tests revealed a tendency of dysphoric individuals to avoid

the threatening faces.

Some later studies used general threat pictures rather than emotional faces. In one

such study, Bradley, Mogg, Falla & Hamilton (1998) used pictures that were either

severe (e.g., assault victims, mutilated bodies) or moderate (e.g., man behind bars,

soldiers) in threat value based on evaluation by judges. Critical trials were the same as the

preceding study, displaying a threat picture paired with a neutral photograph, displayed

side by side for 500 ms. Results showed that HA participants were quicker to react to

probes replacing higher rather than moderate threat pictures, implying a greater vigilance

for higher threat cues. In a subsequent study, Mogg et al. (1998) employed pictures from

the International Affective Picture System (IAPS; Lang Bradley & Cuthbert, 1995) and

reached the same conclusions.

The same authors (Mogg & Bradley, 1999) repeated the study using probe

classification rather than probe position. Probe classification produced three times as

many errors as probe position, and participants were slower by approximately 200 ms in

responding the probes. Mean response times for probe position are in the order of 300-

400 ms and 500-600 ms for probe classification (Mogg et. al, 1998, Mogg & Bradley,









1998b). However, results still provided more evidence in favor of an attentional bias

towards threat stimuli.

Using the pictorial dot probe offered other options to measure the time course of

attentional allocation and bias. An additional means to gain insight regarding direction of

attention was the addition of tracking eye-movement to the basic task. One such study

was undertaken by Bradley, Mogg and Millar (2000); they added eye tracking to the

basic dot probe task using pictures of happy, threatening and neutral facial expressions

displayed for 500 ms. Gaze tracking measured "overt" shifts in attention, that is,

voluntary shifts in attention, while reaction time to probes provided a measure of covert

orienting of attention (involuntary shifts). Dysphoric individuals were faster in

responding to probes replacing threatening stimuli and eye tracking patterns revealed that

they also tended to initially orient to the threat stimuli as opposed to non-dysphoric

individuals.

A masked version of the pictorial dot probe has also been developed (Mogg &

Bradley, 1999), as have studies to investigate the time course of attention by

manipulating stimulus duration. Bradley et al. (1998 a) investigated the time course of

attentional processes and found HA individuals displayed higher vigilance towards threat

faces (but not towards emotional faces in general) when the stimuli were displayed for

500 ms and 1250 ms.

A substantial amount of research using dot probe has been conducted on removing

the uncertainty surrounding information processing biases in social anxiety (review by

Heinrichs & Hoffmanm, 2001). Some studies on this topic have suggested vigilance for

social-threat cues while others have found avoidance, partly due to the difference in









methodologies of the studies. Early studies using social-threat words did not reveal a

clear relationship between social anxiety and attentional biases. Asmundsen and Stein

(1994) were the first to investigate this relationship using social phobics. They used a

modified version of the dot probe; displaying word pairs in top-and-bottom orientation

for 500 ms and instructing participants to read aloud the top word in every trial.

Following stimulus offset, participants were to respond as quickly as possible to probe

onset by pressing the appropriate button indicating probe position. Results indicated that

social phobics responded quicker to the probe regardless of probe location when the

social threat word appeared on the top. Thus, although the study proved that social

phobics selectively attend to socially evaluative words, it suffered from interpretative

problems due to the aforementioned decrease in RT regardless of probe position. As such

the results could also be interpreted as individuals displaying enhanced vigilance after

reading a threat word. Two other studies with similar populations also resulted in no

significant effects towards social threat cues by socially anxious people (Horenstein &

Segui, 1997; Sanz, 1997).

2.2.3.5 Social anxiety

Mansell, Clark, Ehlers and Chen (1999) tested socially anxious individuals under

conditions of socially evaluative threat and no-threat. Participants were divided into

groups on the basis of their social anxiety scores (lower (<8) and upper quartile (>17)

scores on the FNE, respectively). Conditions of social threat were induced by informing

participants that they were to give a speech to a live audience after the test. An equal

number of participants were tested under threat and no-threat conditions. Stimuli in this

case consisted of pictures of faces (happy, threat and neutral) paired with a picture of a

household object. The threat condition induced attention away from emotional faces









(both positive and negative) while the no-threat condition did not find any differences in

attentional bias between the test and control groups. The authors also covaried out the

differences in trait anxiety and depression indices and found an attentional avoidance

effect. The fact that social phobics avoid emotional faces stimuli while other phobics (see

below) direct attention to emotional stimuli lead the authors to suggest that phobics

exhibit attentional biases in directions which reduce the uncertainty around the threat

stimuli. For instance, findings for individuals with high social anxiety have not been

consistent with those obtained from various other groups afflicted by anxiety disorders

and phobias. Lavy and van den Hout (1993) found a similar attentional bias for spider

related words and pictures with spider-phobics, which according to Mansell et al. (1999)

was the best way for individuals to reduce uncertainty about the spider. A social phobic,

on the other hand, breaks eye contact by looking away from the face cue to achieve the

same end result. However, a later study by the same authors (Mansell, Ehlers, Clark, &

Chen, 2002) using threat words as the salient stimuli with high and low socially anxious

college students under conditions of social threat and no-threat did not find any bias

towards or away from the threatening stimuli.

Using pictorial stimuli, Mogg & Bradley (2004) examined social phobics for bias

to threat cues and the time course of their attentional processes. Pictures of emotional

facial expressions served as the emotional cue and were displayed for either 500 ms or

1250 ms. A significant trend to attend to preferentially to negative faces as opposed to

positive or neutral faces was observed for the clinical population in the 500 ms condition.

In the 1250 ms condition however, no bias was found for either the clinical or the control

group.









2.2.3.6 Drug abuse

Lubman, Mogg and Bradley (2000) compared methadone-sustained drug users to

age-matched controls for attentional bias towards drug-related cues. Participants were

shown drug-related pictures (needles, spoons, heroin wraps, etc.) paired with neutral

pictures for 500 ms. The hypothesis predicted the existence of a drug related bias as

posited by some cognitive theories (Robinson & Berridge, 1993); consequently relapse

has been linked to an attentional bias towards drug related stimuli (Wikler, 1965; Siegel,

1979; Stewart et al., 1984; Childress et al., 1986; Baker et al., 1987; Tiffany, 1990).

Findings supported the prediction in that opiate drug users displayed an attentional bias

towards drug related information.

2.2.3.7 Smoking and alcoholism

The same theories incited research for attentional bias in smokers and alcoholics

towards their respective drugs. Townsend and Duka (2001) extended the research of

Lubman et al. (2000) and adapted it to investigate for a bias in non-dependent heavy

social drinkers towards alcohol-related cues as opposed to occasional social drinkers.

Critical trials consisted of an alcohol-related cue (word or picture) paired with a neutral

non-alcoholic cue. All cues were displayed for 500 ms. Results confirmed a bias towards

alcohol related cues in the heavy drinker group. Ehrman et al. (2002) based their research

on the two studies mentioned above and examined whether current cigarette smokers

displayed an attentional bias towards smoking cues as opposed to non-smokers and

former smokers, respectively. They found smokers to have a significantly higher bias

towards smoking cues than non-smokers while former smokers had an intermediate level

of bias.









2.2.3.8 Eating disorders

The cognitive model of Vituosek and her colleagues (Vitousek & Holon, 1990;

Vitousek & Orimoto, 1993) identifies two basic cognitive factors to blame for causing

and maintaining eating disorders; individuals' body image (shape and weight) and the

schema biased processing of the body image. Clearly, the second factor is reminiscent of

the models of Beck (1976) and Bower (1981). Earlier studies on body image and eating

disorders relied heavily on data mainly collected through self-report questionnaires.

Using self-report measures is potentially limiting because it may be confounded by

distortions of self-image and denial (Fairburn et al. 1991; Vitousek & Orimoto, 1993).

The dot probe, on the other hand, can provide an objective measure of attention and

response to food cues. Following this line of reasoning, Reiger, Schotte, Touyz,

Beumont, Griffiths and Russell (1998) examined the existence of a bias toward body and

shape related stimulus words in patients of anorexia nervosa, bulimia nervosa, and

controls. They used words reflecting large or thin physiques paired with neutral words on

critical trials. Individuals with eating disorders exhibited a bias towards words describing

a large physique and away from neutral words and words representing a thin physique.

Taken together, these results may indicate that individuals with eating disorders process

information related to fatness while ignoring information related to thinness. If so, it

could indicate a fear of attaining a large physique despite evidence to the contrary,

explaining why patients of these eating disorders show an aversion to food.

In yet another study, Placanica and her associates (Placanica, Faunce, Soames Job,

2002) tested high and low scorers on the Eating Disorder Inventory-2 (EDI-2) under

fasting and non-fasting conditions for bias towards food stimuli. They found a bias

towards high-calorie foods under the fasting condition across all participants while high









EDI-2 scorers showed a bias to low-calorie (non-fat) foods only when not fasting. This

hunger-driven bias towards high-calorie foods may shed some light on the binge-purge

and cycle found in bulimic-nervosa.

2.2.3.9 Pain and miscellaneous areas

Some other non-traditional areas where the dot probe has been applied of late

include attentional bias towards pain stimuli (Keogh et al, 2001; Dehgani, Sharpe &

Nicholas, 2003) in chronic pain sufferers, towards words related to Irritable Bowel

Syndrome (IBS) for IBS sufferers (IBS; Gutierrez, 2001), to sexual and violent words in

victims of sexual trauma (Bush, 2000).

2.2.3.10 Limitations of the dot probe

Although it has been used with considerable success in various studies with a host

of anxiety and other disorders, the dot probe task has several limitations. The most

glaring insufficiency of the task is that it does not provide a complete picture of the

timecourse of attention but only of attention at the instant of probing.

One of the more serious criticisms of the task, and one it shares with the Stroop

task is that the salient stimuli are presented in the foveal region. Although foveal vision

and attention are not the same, it is believed that it is impossible not to attend to

information presented within a 1-degree radius of fixation. Thus, results of the two tasks

cannot conclusively say whether threatening stimuli attract attention or hold it once they

are detected. However, the task is easy to administer and provides a direct reading of

attentional bias at the instant of probing.

2.3 Connectionist Models of Attention

Williams et al., (1997) identified two main issues concerning the study of

attentional biases: the cause and the mechanism. Causes refer to the reasons why









attentional biases manifest themselves only in some people under certain conditions.

Mechanisms refer to the point in the information processing system at which they act.

The first issue has been addressed by different paradigms used to study attentional biases.

For example, robust relationships have been established between trait anxiety, state

anxiety, stress and their affect on attentional biases using the dichotic listening paradigm,

the Stroop and dot probe tasks. Studying mechanisms, on the other hand, has not been as

straightforward. Developing a clear understanding of the mechanisms is important to

understand attentional biases more thoroughly and devise more effective treatments for

the various disorders.

An attractive method to study mechanisms of various constructs is through

computer simulations. Developing such a simulation allows researchers to intervene,

change variables and measure their effect. Neural Networks (NN) models (also known as

Parallel Distributed Processing (PDP) models) are computational modeling paradigms

based brain operations and are the preferred modeling paradigm when simulating

attentional biases on computers. In fact Williams et al. revised their 1988 model in 1997

to explain in PDP models (Williams et al., 1997).

The second analysis tool employed in the current study is a Bayesian belief

network, or Bayesian network (BN) for short. BN are probabilistic graphical models. The

current study represents the first known attempt to use BN to arrive at probabilistic

relationships between variables involved in the dot probe task. Current popular

applications of these models are in the fields of mainstream computer science (e.g.,

datamining- discovering relationships between relationships from data, expert diagnostic

systems, etc.) and business and finance (e.g., risk analysis for insurance and other









projects, stock market prediction). Bayesian networks' application to cognitive reasoning

has been rather limited, mainly said to be more suited to higher order reasoning tasks than

simulating lower, automatic processing tasks. One of their most widely known

applications is in the sometimes annoying Microsoft Office Helper and troubleshooter.

BN are most applicable in areas where relationships between variables are known (this is

explained below). BN also offer an intuitive method of modeling the relationships

graphically. The current study will use BN to develop a causal model of attentional bias

as per the dot probe task and then fine-tune the probabilistic relationships between the

variables.

In this section, the basics of the main NN models developed for studying

attentional bias, the models to simulate the Stroop task by Cohen et al. (1990) and the

extension of the same to the emotional Stroop by Matthews and Harley (1996) are

summarized. The section first explains the theory and working ofNN. The two models

are then discussed in detail. The theory and working of BN are explained next along with

an example of how they will be applied in the current study.

2.3.1 Neural Networks

A neural network is a massively parallel distributed processor made up of simple
processing units, which has a natural propensity for storing experiential knowledge
and making it available for use. It resembles the brain in two respects:

Knowledge is acquired by the network from its environment through a learning
process.

Interneuron connection strengths, known as synaptic weights, are used to store the
acquired knowledge. (Haykin,1998, p.2)

2.3.1.1 Overview

A NN consists of a number of small processing elements that are also referred to

as neurons. Each neuron is capable of performing only very simple calculations;









computing the input and using a transfer or activation function to compute an output. A

single neuron in the human brain is much slower than a microprocessor (by about an

order of 106, with a neuron taking 10-3 s per operation compared to the 10-9 s of a

microprocessor). The brain overcomes this disadvantage of speed by using parallel

processing. Each neuron is connected to numerous other neurons, with the connections

between them known as synapses allowing simultaneous parallel activation of varying

neural circuits. Shepherd and Koch (1990) estimated the number of neurons in the brain

at 10 billion with 60 trillion synapses. As such, NN try to emulate this natural parallelism.

Each synapse has a strength associated with it; referred to as the "interneuron connection

\ilengith or synaptic 1 eighn"' (Haykin, 1998, p.2). Each units' input is a summation of

the weighted output of all the other active units that project to it. Synaptic weights can be

positive (excitatory) or negative (inhibitory). Clearly, these weights are the most basic

variable in a NN; they are adjusted according to the application area of the NN using a

learning algorithm.

2.3.1.2 Learning

Learning in a NN is the process of adjusting the synaptic weights according to the

variations in the learning data (i.e., the problem). Indeed, learning paradigms are

classified into learning with a teacher (supervised learning) and learning without a

teacher (reinforcement and unsupervised learning) (Haykin, 1998). In supervised

learning, for example, the NN is provided with an input and the known result for that

input (called target output). The network computes the output based on the input (called

computed output) and compares it against the target output. The weights are adjusted

using a function to minimize the error between the target and computed outputs. A

detailed explanation of supervised learning is provided in the next section. Alternatively,









when learning without a teacher, the network uses one of two techniques: (1)

reinforcement learning. where the NN has an in-built "critic" (some scalar index of

performance) and learns by minimizing the scalar index or (2) unsupervised learning

which, instead of a critic has a task independent measure that optimizes the free

parameters of the network. Specifically, in unsupervised learning, the network uses the

task independent measure to find statistical regularities in the input data enabling it to

form internal representation of data to automatically derive new classes of data (Becker,

1991). For a full discussion on supervised and unsupervised learning, see (Haykin, 1998).

2.3.1.3 Supervised learning.

Supervised learning consists of two phases, a training phase followed by a test

phase. The training phase consists four steps that culminate in the network being able to

compute the correct output for each of the input cases. The steps are:

1. Input data with known outputs (target outputs) to the network.

2. Allow the network to compute its output (computed output) based on the given input.

3. Compute the difference between the computed output and the target output.

4. Use the learning algorithm to adjust the synaptic weights based on the magnitude of
the error difference.

The test phase supplies new inputs not previously seen by the network.

2.3.1.4 An example of supervised learning.

An example of supervised learning is a model to predict whether it will rain on a

particular day or not. The first step is to identify the independent and dependent variables

in the model and choose the NN architecture2 for the problem. In this example, the inputs


2 Architecture of a NN refers to how the neurons in the network are connected to each other. Three basic
architectures are single-layer feedforward networks, multi-layer feedforward networks and recurrent
networks. Multi-layer feedforward network architecture is the one most commonly used in supervised
learning including in the current study and in the simulation of the Stroop (Cohen, et al. 1990) and the









are the four of the most basic variables known to affect weather on a given day, pressure,

humidity, temperature, and wind-direction. The output consists of two nodes, rain or no-

rain; signaled by activation of the respective nodes. The next step is to initialize the

network by assigning weights to the inter-neuron connections. To start with, these

weights may be generated randomly within some range. Once the network is initialized, it

must be trained, constituting the third step. Input for the training phase consists of the

four input variables and the value of the observed (target) output for a given day (i.e.,

whether it rained or not). The training phase involves the network computing the output

for a large number of training input cases, and adjusting the synaptic weights accordingly

until the computed output matches the target output for each case. The successful

completion of all four steps culminates in the network being ready to predict whether or

not it will rain on a given day given the temperature, pressure, humidity and wind-

direction for that day.

2.3.2 Details and Theory

2.3.2.1 Overview

Figure 2.4 shows a basic multi-layer feedforward NN (multi-layer refers to multiple

layers of weights) that uses the back-propagation algorithm for learning (also known as

the backpropagation network (BPN) or the backpropagation architecture.

The BPN consists of an input layer, one or more hidden layers and one output layer.

Figure 2.4 provides an example of a network that contains an input layer of two nodes (Ii

and 12), one hidden layer of four nodes (HI through H4) and one output layer of two

nodes (Oi and 02). Input and output neurons are always in one of two states,firing


emotional Stroop (N Litthi\ si & Harley, 1994). For detailed information on network architectures see
Haykin (1994).









(active) or not-firing (inactive), whereas hidden neurons, can have a discrete output or

use the activation level itself as the output for the node (explained in detail below). Input

to the network is provided by applying an activation pattern over the input nodes. Output

of the network is given by activation of one of the output nodes. The network has one

input unit for each input of the problem being modeled, and one output unit for each

possible output (e.g., the NN in the weather example in the previous section contains four

input variables and two output variables). The number of hidden layers and the number of

units in each layer is also problem specific, but typically the number is between the

number of input nodes and the number of output nodes; lesser than the number of input

units and greater than the number of output units (Blum, 1992). Hidden nodes provide

non-linearity to the network.

A BPN is considered filly connected if every neuron in one layer is connected to

every neuron in the next layer. Figure 2.4 is an example of a fully connected BPN. When

the neurons in one layer are only connected to certain neurons in the next layer, the BPN

is considered partially connected. In either case, there are no connections between

neurons in the same layer.












Output r o 0
Layer



2nd Weight w11
Layer (w2) / 12 W 41



Hidden Hi H2 W 31 H3 HH4
Layer
W 21 1 22 W14

1st Weight W24
Layer (w1) 23


Input Layer{
1, 12

Figure 2.4 A general multi-layer backpropagation neural network.

2.3.2.2 Notation

This section describes a notation based that used by Haykin (1998) to clearly refer

to weights on any connection in any of the weight layers and to refer to any unit an any of

the three layers of units. As mentioned earlier, a NN consists of layers of units (input,

hidden and output). Weights are denoted by wny which is the weight w on the nth layer of

weights between nodes i andj (note that nodes i andj are in different layers of units, for

instance, the input and hidden or hidden and output layers). For example, the NN of

Figure 2.4 consists of two layers of weights; the first (denoted by w1) between the layer

of input units and the hidden layer and the second (denoted by w2) between the hidden

and output layers. Therefore the weight of the connection between thefirst unit in the

input layer and the third unit in the hidden layer is denoted by w113. Similarly, the weight









on the connection between the second unit in the hidden layer unit and thefirst output

unit is denoted by w 21. Input to a unit (not shown) is denoted by the letter x; so x,

represents the input to thejth unit in a layer. Activation level of the unit is denoted by a,

so aj denotes the activation level of thejth neuron.

2.3.2.3 Initialization

The network can be initialized by randomly assigning randomly generated weights

to the connections between units. Alternatively, the designer can assign weights to the

connections according to the problem. In either case, the weights are adjusted according

to the problem domain using the learning algorithm during the training phase.

2.3.2.4 Node Details

Figure 2.5 is a detailed representation of a node of the network of Figure 2.4. The

figure refers to the third node in the hidden layer of the network; receiving input from the

two input units (I, and I2) and transmitting the result to the two output units (not shown).

As illustrated, the processing unit performs two basic tasks:

1. Computes the net input (denoted by x3 with the computations performed by

the summation unit).

2. Computes the activation level from the net input (denoted by a3, using the

transfer function to perform the computations).

Output of the node may or may not be the same as the activation level.

2.3.2.5 Net input

The net input to a hidden unit is typically the sum of the product of the output of

each input unit and the synaptic weight of the connection between the two.

Sometimes a bias value (b) may be added to the net input of each node to lend















X3+b a3

I2 1
Sy3

Summation Unit Transfer
Function

Input Layer 1st Weights 3rd Processing Unit
Layer of Hidden Layer


Figure 2.5 Details of a simple processing unit of a neural network.

variability to the network. The bias can be a constant set by the experimenter so it is the

same for every node, or a random number generated from within a specified range.

Therefore in this case, the net input is:

X3 = IW 3 +2Iw +b --2.1

where I/ and 12 are the outputs of the input units. The above equation can be

generalized to give the net input for any arbitrary node (/th node of the nth layer) as:

xJ = -arI +b --2.2


where a, is the activation of the units in the previous layer.

2.3.2.6 Activation level

Computing the activation level consists of applying the transfer (activation)

function to the net input. A BPN requires the transfer function to be non-linear,










continuous and monotonous (i.e., differentiable at any point of the curve) (Haykin, 1998;

se also Cohen, et al. 1988). A class of functions known as sigmoid functions fulfills these

requirements and the function that is most commonly chosen as the activation function

among the functions of this class is the logistic function given by:

Figure 2.6 Graph of the logistic sigmoid function






1.0

0.8

0.6

0.4

0.2

0.0
-5 -4 -3 -2 -1 0 1 2 3 4 5
Net Input

1
Activation, f(xi )= a --2.3
1+e X

Figure 2.6 depicts the graph for the logistic function of equation 2.3. Note that the

slope of the function is the highest when the net input is zero and increases more slowly

the higher the value of activation.

2.3.2.7 Output

As mentioned above, the output of the node depends on whether the node is a

hidden or output node. For a hidden node, the output of the node is usually the same as

the activation level. However, a threshold value is set for output nodes (by the

experimenter) and the node fires if and only if the activation level of the node exceeds the









set threshold. Alternatively, the output may be selected as some function based on the

activation level of an individual unit or all the units in the output layer. The number of

output units of the network depends on the problem being modeled and the number of

units that can be active simultaneously depends on the problem parameters. In short, The

network loops until an output is obtained (i.e., one of the nodes fires). Cohen et al. (1990)

used one such function in their model; the process is explained in the next section.

2.3.2.8 Training

During training, the NN is supplied with the target output for each input pattern.

The network computes the output (computed output) and the learning algorithm

compares the computed output with the target output to calculate the error. The learning

algorithm used in the two simulations of the Stroop task is known as the delta rule. Error-

information is then propagated back through the network and each unit of the network

adjusts the weights of its connections according to some error-minimizing function (e.g.,

gradient-descent, so called because the function estimates the direction in which to move

down the slope of the function to as to minimize the function). Error correction may be

carried out after each of the

Figure 2.7 shows the flow of computation and weight-correction for a BPN.

Backpropagation algorithm is by far the most popular error driven learning algorithm.

Summarizing, the training phase consists of the following steps:

* Activate the appropriate input units.

* Compute the output. The network is allowed to run until one of the output units
fires.

* Compute the error (difference between the computed and target outputs).

* Propagate the error information backwards through the network to all units














Output r0 0,
Layer



2nd Weight
Layer (w2)



Hidden
Laver {


1st Weight
Layer (w) i


Input Layer{
I1 12

Figure 2.7 Flow of activation (solid lines) and error (dotted lines) in a multi-layer
backpropagation neural network.

and adjust the synaptic-weights using the backpropagation algorithm. Error correction

may be performed after a single input activation is presented to the network; or after all

the input patterns have been presented to the NN. In the latter case, the network performs

the corrections based on the total error (the mean-squared-error [see Haykin, 1998]) for

all input patterns, which is the square root of the mean of sum of the squares of error for

each input pattern. Mathematically,



Serror2 + error +...+ error
mse = 1 2--2.4
n

The network performs error-correction until the error falls within the specified limit

set according the problem.









2.3.2.9 Testing

Once the training is complete, the network is ready to accept new inputs (as

opposed to the training data) and produce an output.

2.4 Connectionist Models of the Stroop Task

Two PDP models of the Stroop task have been developed to date, the first by

Cohen et al. (1990) that simulated the findings of the basic Stroop task and the second, a

simulation of the emotional Stroop, reported by Matthews and Harley (1996). This

section discusses the design of both networks, along with issues concerning training and

testing of the two. In order to be considered a successful simulation of the Stroop task, a

model must replicate the main empirical findings of the task.

* Word reading is faster than color naming. Mean time to read a color word is 350-
450 ms while naming a color patch of a row of X's takes about 200 ms more (550-
650 ms) (Dyer, 1973; Glaser & Glaser, 1982).

* Word reading is not affected by color ink. Color of the word to be read has virtually
no affect on the time to read the word.

* Words can influence color naming. Content of the word interferes with color
naming; conflicting words cause a substantial increase (variable but commonly 100
ms) in the RT to name colors. Conversely, congruent words facilitate performance
in color naming, reducing RT by 20 ms (Regan, 1978) to 50 ms (Kahneman &
Chajczyk, 1983).

* Facilitation is less than interference. Although congruent stimuli have been used
only sparsely, general findings are consistent with the pattern mentioned above in
that the amount of facilitation (20 ms) is much less than interference (100 ms).

2.4.1 The Cohen Model

Cohen et al. (1990) used a partially connected PDP model to simulate the Stroop

task (Figure 2.8). The model produced the main empirical findings of the Stroop task.

Input to the network consisted of specifying the task and task parameters (i.e., whether to









perform color naming or word reading and the ink color and the word). Output consisted

of generating the response for the input through activation of the correct ink color for the

color-naming task and the correct word for the word-reading task. The Cohen model

computed the time course of a psychological process by presenting results in terms of

reaction time (RT), computed by deriving a linear relationship between the number of

iterations taken by the network to compute the output and typical RT for the task. As

such, the authors required the network to mimic the variability in reaction times of human

participants performing the Stroop task. This mandated some changes to be made in the

way each unit computes input and the selection of the final output by the network.

2.4.1.1 Structure

Cohen et al. (1990) used a partially connected BPN, consisting of two processing

pathways, one for color naming and one for word reading. Each of the pathways can be

thought of as a distinct neural network with both competing for the final output, achieved

by connecting the hidden layer to both output units (see Figure 2.8). The network

contained six input units to specify ink color, task and the words to be read, and two

output units representing the possible outputs (i.e., red or green). The model could handle

only two words, "Red" and "Green", printed in two possible ink colors, RED and

GREEN. Inputs were presented as a pattern of activation over the input nodes.

2.4.1.2 Initialization

Cohen et al. (1990) assigned small, random weights to the connections between the

hidden and input layers and intermediate values (either +2 or -2) to connections between

the input and hidden layers. In the latter case, values were chosen to obtain a

straightforward mapping from the input layer to the hidden layer.












RESPONSE

"red" "green"


Ii 12 l5 1 l6 I
red green 3 14 RED GREEN
Input layer C Wr
Color Word
INK COLOR Naming Reading WORD READING

TASK DEMAND

Figure 2.8. Neural network model for simulation of the Stroop task

2.4.1.3 Net input

Each unit computed net input in a similar manner to the one described in equation

2.2. Two changes were made to the manner in which net input was computed for each

unit; the first was to allow the network to simulate the time course of a psychological

process. The initial change was based on the cascade models (McClelland, 1979), which

also simulated the time course of psychological processes; net input at any instant of time

t was defined as the running average of its net input over time. Mathematically:

x,(t) = rx (t)+(1- r)x(t 1) --2.5


where, T is a rate constant and,









x, (t) = a, (t)w, + b --2.6


Note that equation 2.6 is the same as equation 2.2 except that a,(t) is the activation at time

t. Additionally, using this function guaranteed that the network would always reach a

stable asymptotic state and result in an output.

The second change was made to add variability of performance to the network; a

normally distributed random bias was associated with each hidden and output unit and

added to the net input (denoted by b in equation 2.6).

2.4.1.4 Activation

The logistic function (equation 2.3), applied to the net input computed according to

equation 2.6, was used to compute the activation. Mathematically,


Activation, f(x, (t) = ai (t) = --2.7
1+e xj(t)

Again, note the only difference between equation 2.7 and equation 2.3 is in the

value of the net input.

2.4.1.5 Output

Output of the network was indicated in the same way as a typical BPN, by the

firing of an output node (i.e., "red" if the node representing "red" fired and "green" if the

other node fired). Cohen et al. (1990) introduced variability in this step by making the

firing of the output unit dependent on the result of a random walk (Link, 1975) or

diffusion process (Ratcliff, 1978). Adaptation of these processes to computing the output

of the network consisted of associating evidence accumulators with each of the output

units. The accumulators were set at 0 at the beginning of each trial and a small amount of

evidence was added at the end of each time step; evidence added was random and









normally distributed with mean / based on the difference between the activation of the

unit and activation of the most active alternative and fixed standard deviation (a = 0.1).

So for the ith output unit, the mean ti is given by

/u, = a(a, max(a,, )) --2.8

a is the rate of accumulation of evidence and was set at 0.1 through all their trials.

The threshold was set at 1.0 for the evidence; so the output unit fired when the

evidence associated with a unit exceeded 1.0.

2.4.1.6 Training

One difference between training the Stroop model and the weather example cited

earlier was that the training in this case was completed separately on the word reading

and color naming tasks, rather than both tasks at the same time. An input pattern

consisted of the ink color or the word and the task to be performed. So an input for the

color-naming task with color "red" was represented by "RED-COLOR-NULL",

activating the input unit for color "red" and the task demand unit (TDU) for "COLOR

NAMING" only. The target output in this case was "red". The network was then allowed

to reach an asymptotic level of activation and generate an output and correct the weight

in accordance with the error between the computed and target outputs using the

backpropagation algorithm.

The Cohen model differed from a typical BPN in initializing and updating the

weights. Firstly, connections in the first layer were randomly assigned values of either +2

or -2. Secondly, weights on the connections between the TDUs and the intermediate

units were kept constant (and not allowed to be changed during training) so that the









activation of the TDU did not provide any extra information to the intermediate units.

However, the authors suggested that these could be learned.

One training objective was to make word reading more automatic than color

naming, achieved by training the network on ten times as many word-reading stimuli than

color naming stimuli, allowing it to strengthen the word-reading connections much more

than color-naming ones. Table 2.1 lists all the training patterns.


Table 2.1: Input patterns and corresponding outputs used for training the network by
Cohen et al. (1990)

2.4.1.7 Testing

Testing involved providing all inputs for the task (color, word and task) to the

network and allowing it to cycle through until the output reached an asymptotic value. In


Ink color (Input) Word (Input) Task Condition Output
Red RED WORD READING Congruent RED
Green GREEN WORD READING Congruent GREEN
Red GREEN WORD READING Incongruent GREEN
Green RED WORD READING Incongruent RED
Red GREEN COLOR NAMING Congruent RED
Green RED COLOR NAMING Congruent GREEN
Red RED COLOR NAMING Incongruent RED
Green GREEN COLOR NAMING Incongruent GREEN
all, the network was tested on 12 different input patterns (listed in Table 2.1) representing

every possible condition, for both color-naming and word-reading. The conditions tested

were congruent (word same as color), conflict (different word and color) and control

(only the color or the word depending on whether testing is for color naming or word

reading). A conflict condition of naming ink color for the word "Green" printed in "Red"

ink was presented to the network as activation pattern "RED-COLOR-GREEN" (i.e.,

activating nodes representing ink color "red", word "green" and color naming TDU).

Cohen et al. (1990) recorded the number of iterations it took the network to reach an









asymptotic activation of the output units and used it to derive a relationship between the

number of iterations and the reaction time by comparing the number of iterations against

established reaction times for each condition. Naturally, this meant the relationship

between the number of iterations and RT was dependent on the task being simulated.

2.4.1.8 Simulations and results

Cohen et al. (1990) performed six different simulations to test findings of the

Stroop task in four different categories and explained those in terms of the PDP model.

The four categories were:

1. S. eigilt ofprocessing which primarily explained the main empirical
findings of the Stroop task on the basis of connection strengths.

2. Stimulus onset asynchrony (SOA) effects, which investigated observing
interference even when the ink color was displayed before the actual word. This
simulation was the only one not in agreement with actual data. Specifically, the
model displayed some influence of color on word reading when the color is
presented early.

3. Practice effects: The simulation was based on the study conducted by
MacLeod and Dunbar (1988) who trained individuals to associate shapes with
colors, creating a novel task which the individuals had not practiced before. The
Stroop task was then constructed in which individuals were presented with shapes
in different colors and were required to name color the shape was originally
associated with. Results indicated that practice on associating colors with shapes
increased performance on color naming the shapes in the Stroop task consistent
with the Power law. Simulation of this task included two different simulations
which investigated the Power law and practice in the Stroop task and developing
automaticity with practice. The first of the two simulations plotted RT as a function
of number of training trials (N) and found performance of the network increased on
color naming the shapes according to the Power law.

4. Allocation of attention: The final two simulations tested the affect of
attention allocation to performance on the two tasks. Researchers have proposed
somewhat opposing views on attention allocation and its affects on performance.
Some researchers define automatic tasks as requiring absolutely no attention
(Posner & Snyder, 1975; Shiffrin & Schneider, 1977), going so far as saying lack of
attention should not influence performance on such tasks (Posner & Snyder, 1975),
while others have challenged this claim, saying few, if any, processes can function
without attention (Kahneman & Treisman,, 1984; Logan, 1980).









Cohen et al. addressed the issue with their model. In the first of two simulations,

they performed the two tasks on their model with varying degrees of attention allocation

(activation of the TDUs) and found that color naming required more attention than word

reading to maintain a given level of performance. More importantly, however,

performance on both tasks degraded by reduced attention. In the second of the two

simulations, the authors investigated response-set effects. More specifically, they

evaluated whether words and objects that are not part of the response set cause

significantly less interference than those that are (e.g., the word BLUE is never a correct

response in the current simulation and so is not a part of the response set). The authors

successfully simulated the picture-naming task (Dunbar, 1985) and observed significantly

less interference for words that were not part of the response set.

Williams et al. (1997) updated their earlier model (Williams et al., 1988) within a

PDP framework following the simulations by Cohen et al. (1990). They re-

conceptualized the ADM as the input units, assigned the task of tagging input with a

threat value and the RAM as the TDU. Despite these revisions, their core assumptions of

the interaction between state and trait anxiety remained virtually unchanged.

Matthews and Harley (1996) built upon the model of Cohen and colleagues (1990)

by adapting it to simulate the emotional Stroop. However, their focus was on trying to

explain the cause of attentional bias, and as such they were not concerned with adding

variability to their model.

2.4.2 The Matthews and Harley Model

Matthews and Harley (1996) extended the Cohen model by applying it to the

emotional Stroop task. The authors set realistic objectives for the simulations, keeping in

mind the lack of simulations and other investigations into the mechanisms of the task.









Their main objective was to investigate three different mechanisms for generating

attentional bias (exposure, intensity and attentional), based on different explanations of

attentional biases. Simulating the emotional Stroop involved changing the network to

present emotional words as inputs. Also, the network was not designed to simulate the

time course of attention, that is, in contrast to the work of Cohen et al. (1990), Matthews

Harley (1996) did not present results by comparing RT but compared relative activation

of the output units. Details are explained in the sections below.

2.4.2.1 Hypotheses

As stated, the model tested three qualitatively different explanations for attentional

biases. The first, known as the exposure hypothesis, proposed that repeated exposure to

emotional stimuli lead to an attentional bias towards emotional stimuli causing an

anxious person to be more practiced, and therefore more automatic, in reacting to

emotional stimuli.

The intensity hypothesis was second viable alternative, and explained the basis of

attentional biases as distressed individuals perceiving the same emotional stimuli as more

potent (higher intensity) than normal individuals, and therefore placing a higher priority

on processing that information. The hypothesis was further branched into state and trait

portions, with high state anxiety individuals perceiving higher intensity only during test

conditions while high trait anxiety individuals felt the same (higher) intensity all the time.

The third hypothesis stemmed from Matthews and Wells (1995) explanation of

observed interference in the Stroop task. They suggested that attentional bias occurs due

to a coping strategy adopted by distressed individuals to monitor potential sources of

threat. Arguably, the coping strategy leads such individuals to pay more attention to









emotional stimuli, which in turn causes larger interference effects. This called for

activation of the task demand unit during testing.

2.4.2.2 Structure

Matthews and Harley (1996) followed an evolutionary approach, extending the

Cohen model for the emotional Stroop. After two unsuccessful architectures (Figure 2.9

(a)) that did not yield satisfactory results for standard Stroop interference, they arrived at

the final model (Figure 2.9 (b)). The first model was a straightforward extension of the

Cohen model, while the final architecture featured extra connections as well as an

additional TDU to monitor threat. The final model had nine input units, six hidden units,

and five output units.

As can be seen from Figure 2.9, input units represent semantic features of the word

rather than the word itself. So each word was presented as activation of a unique

combination of input units, and the network was trained to output the word corresponding

to the semantic units activated. Color indicated a color word and color type indicated the

degree of redness, thus by activating both the units simultaneously word "red" was

represented. "Monster" is associated with a large object (being) and negative emotion and

therefore is presented to the network by the activation of (large) SIZE and (negative)

EMOTION. The semantic codes words for all the words used by the network as seen by

the output produced are listed in Table 2.2. Presenting input in this manner had two

distinct advantages; firstly, it was consistent with psycholinguistic theories stating speech

processing is a two level process. Secondly, it allowed the network to learn semantic

similarities between words.









2.4.2.3 Initialization

The network was initialized using the same as the initialization method used by

Cohen et al. (1990).

2.4.2.4 Input

Since the network was not intended to model the RT of the psychological process,

Matthews and Harley used the basic BPN equations to compute net input (equation 2.2)

and activation (2.3) for each unit.

2.4.2.5 Output

Obtaining output was rather straightforward in this case, given that the output

produced in the first iteration of the network became the final output and was used for

comparisons against baseline conditions.

2.4.2.6 Training and testing

Differences in architecture apart, both networks implemented the BPN architecture

and were trained using the same basic algorithm. Presenting all training patterns to the

network is called an epoch. Matthews and Harley trained the network for 400 epochs

(i.e., cycling 400 times through all the training patterns shown in Table 2.2). The number

of training patterns of each type used for training and the activation values depended on

the hypothesis. Training patterns for the baseline condition are displayed in Table 2.2.

The table highlights an interesting distinction in the training approaches for the two

networks; the Matthews and Harley network was trained to ignore input in the absence of

a task specification, that is, when a TDU was not activated. Otherwise, Matthews and

Harley still used Cohen et al.'s (1990) approach to make word reading more

automatic than color-naming, training the network more on word reading than color





























a. Models 1 and 2


b. Final Model


Figure 2.9 Matthews and Harley Model (a) the first two models. The dotted lines were
connected in Model 2 while non-existent in model 1, (b) model 3 shared the
same connections for the 2nd weight layer with model 1. Connections that
differ in layer 1 are shown as solid lines while those carrying over from 1 and
2 are shown in dotted lines.










naming. Results were obtained by comparing the activations of the output unit for each

hypothesis condition against baseline activations. The authors manipulated training sets

for each of the hypotheses. Exposure condition involved doubling (chosen arbitrarily) the

Table 2.2: Training patterns and number of times each condition was presented to the
network to train for the emotional Stroop task.

Stimulus Input TDU Activated Output Repetitions
Color + Color Type Word Reading Red 16
Color Word Reading Green 16
Emotion Word Reading Spider 16
Size Word Reading House 16
Emotion + Size Word Reading Monster 16
Color + Color Type 2
Color 2
Emotion 2
Size -
Emotion + Size 2
"Red" Color Naming RED 1
"Green" Color Naming GREEN 1
"Red" + Emotion Color Naming RED 1
"Green" + Emotion Color Naming GREEN 1
"Red" + Size Color Naming RED 1
"Green" + Size Color Naming GREEN 1
"Red" + Emotion + Size Color Naming RED 1
"Green" + Emotion + Size Color Naming GREEN 1
"Red" -
"Green" 2
Color + Color Type Threat Monitoring Unit 2
Color Threat Monitoring Unit 2
Emotion Threat Monitoring Unit Spider 2
Size Threat Monitoring Unit 2
Emotion + Size Threat Monitoring Unit Monster 2


number of training patterns of emotional word reading. To train for the intensity

condition, Matthews and Harley changed the input from 1 to 8 for appropriate units,

simulating hypersensitivity to the stimuli. Finally, attentional manipulations did not entail

any changes in training but the unit was set to a low positive (0.3) value during testing.

The input patterns for which no output is listed were used to train the network to produce

an output only if a TDU was activated.










2.4.2.7 Results

The three test mechanisms tested in this simulation are stated above, namely

exposure, intensity and attention mechanisms. The first condition was further divided

into two parts, emotion word exposure and emotion task exposure. The former simulated

performance on the two tasks after increased exposure (presenting the appropriate

patterns 32 times as opposed to 16 during training) to reading emotional words. Results

found an increase in reading emotional words while almost no effect was observed for

color naming. The latter condition trained the network to respond to emotional words

only when the TMU was activated, indicating an acknowledgement of the threat value of

the word. This manipulation resulted in a marginal impairment of color naming and a

similar improvement in word reading. However, the TMU was not activated during

testing.

In intensity manipulations, the researchers trained the network to simulate chronic

hypervigilance to threat words by increasing the activation of the threat words from 1 to

8, resulting in stronger emotional Stroop interference but impaired performance on

reading emotional words.

The final condition tested performance while attending to the emotional content of

the words for the tasks (word reading and color naming). The TMU was set to a low

positive value (0.3) while testing to simulate concurrent attention to the threat value of

the word, resulting in a significant increase in interference in color naming emotional

words coupled with a small impairment the same for neutral words. The same

manipulation resulted in a minor impairment of reading neutral words while having

almost no effect on reading color words. All results were consistent with the findings of









emotional Stroop interference having a smaller magnitude than standard Stroop

interference.

2.4.3 Pros and cons of using PDP models

Although computational models in general, and PDP models in particular are

attractive methods to simulate human behavior, to understand underlying mechanisms,

they are not without advantages and potential pitfalls. O'Reilly and Munakata (2000)

summarized the major advantages and disadvantages of using PDP models.

2.4.3.1 Advantages

1. Models can aid in understanding phenomena and their mechanisms. For example,
the Cohen, et al. NN explained some findings of the Stroop task in terms of the
weights on the connections between units.

2. Models deal with complexity explaining phenomena that would be impossible to
explain verbally.

3. Models are explicit. Models force researchers to think clearly about the
assumptions made in the models. Further, the results obtained from these models
are clear and cannot be written off as some other processes interfering in the main
task. An example is the lack of conformity between the results obtained for SOA
effects in the Cohen model.

4. Models allow control. Different variables can be assigned different values, using
different activation functions and so on.

2.4.3.2 Criticisms

1. Models are too simple. Models have to simplify a lot of the variables in the task.
Further, usually models involve only the variables used in the tasks and no
extraneous variables are modeled. They do not model the biological and physical
variables in any detail.

2. Models are too complex. Some researchers believe that models are too complex
to be useful in explaining their behavior. This is especially true for NN, although
it is clear at an abstract level that the connections between the units in different
layers are strengthened, they do not really provide an explanation of what the
intermediate units represent. In essence, NN follow a black box approach to
modeling.









3. Models can do anything. Given enough data, PDP models can be trained to
simulate just about any condition, which is analogous to a theory that explains
everything.

2.5 A Belief Network Model of Attentional Bias in Dot Probe Paradigm

Neural networks are founded in theories of neuroscience and mimic the architecture

of the brain; so they offer an intuitive way to simulate attention and analyze its

underlying processes. One limitation of such models however, is their "black box"

approach, meaning that although one has access to the synaptic weights, interpreting their

values is not straightforward. Questions still abound regarding the role of the hidden units

and meaning of the weights on synapses connected them. For example, both models of

the Stroop task discussed above (Cohen et al., 1990; Matthews & Harley, 1996) list the

weights on the connections between input and hidden units and between hidden and input

units and how they are strengthened or weakened depending on the training data.

However, hidden units do not represent discrete variables; therefore knowledge of the

connection strength cannot be interpreted in terms of a relationship between input and

output variables.3

Further, as mentioned earlier, research into the causes and mechanisms of

attentional biases have yielded very consistent and robust relationships between different

variables of attention and the paradigm used to test it. However, no studies attempting to

quantify the said relationships have been found. The current study attempts to do just

that; determine probabilistic (or belieJ) values of variables involved in attentional biases

from the dot probe perspective.



3 As an illustration, consider the fact that the model of the Stroop task could have been implemented using
a fully connected BPN as opposed to the partially connected ones that the authors used. In light of this
evidence, what is the significance of the connections and the weights on those connections.









A Bayesian network (or beliefnetwork (BN)) is a tool that allows simple and

elegant modeling of a system with known variables and established relationships. A BN

is a graphical model that encodes probabilistic relationships among a set of variables

(Heckerman, 1996).

Graphical models are a marriage between probability theory and graph theory.
They provide a natural tool for cdetling n ith two problems that occur throughout
applied il, tIeall, tii \ and engineering -- uncertainty and complexity -- and in
particular they are playing an increasingly important role in the design and
analysis of machine learning algorithms. Fundamental to the idea of a graphical
model is the notion of modularity -- a complex system is built by combining simpler
parts. Probability theory provides the glue whereby the parts are combined,
ensuring that the system as a whole is consistent, and providing ways to interface
models to data. The graph theoretic side of graphical models provides both an
intuitively appealing interface by which humans can model highly-interacting sets
of variables as well as a data structure that lends itself naturally to the design of
efficient general-purpose algorithms (Jordan, 1988)

Clearly, understanding BN requires an understanding of the basic laws of

probability and graph theory, both of which are explained in the sections that follow.

2.5.1 Nothing is Certain

Logic provides the tools for reasoning with absolutely certain values, like "if it

rains, the grass will be wet". Such a statement deals with absolute certainty, that is, if it is

known that it is raining, the grass will be wet. Logical reasoning, however does not work

well with uncertain events. Consider the problem of trying to predict whether or not it

will rain given that it is cloudy. Two uncertain variables complicate prediction in this

case: the state of cloudiness (e.g., the number and type of clouds) and the probability of

rain given the state of cloudiness. Is the statement, "if it is cloudy, it will rain" an

absolute certainty? If the number of mistakes made by the National Weather Service

considered, the clear answer is "no." Weather prediction has to deal with uncertainties;

statements like, "if it is cloudy, it will probably rain." The same is the case with the vast









majority of contexts as few real world problems have absolute certainties associated with

them. Statements like "you will fail the course because of your laziness", or "reckless

driving causes accidents" (from Pearl, 2000, p.1) reflect some amount of uncertainty.

Surely not all lazy people fail the course, and not all instances of reckless driving result in

accidents. What these statements imply is that the particular actions mentioned increase

the likelihood (or probability) of the consequence. The goal is to compute the probability

in each case.

Probability implies doubt, lack of regularity, exceptionality. In other words, it is a

measure of uncertainty. Logical reasoning offers four different logical connectives,

namely conjunction ("both the grass and the pavement are wet"), disjunction ("either the

grass is wet or it is not"), implication ("ifit rains, then the grass will get wet"), and

negation ("the grass is not wet"). Combining two statements can lead to an inference

about an event not explicitly specified; for example, combining "ifit rains, then the grass

will get wet" and "the grass is not wet" lead to the conclusion that it did not rain (Jensen,

2000). Probabilistic reasoning warrants development of a similar set of rules on the lines

of logical operators to combine probabilistic values. For instance, to compute the

probability of rain when the probability of "rain when cloudy" is 0.8 and the probability

of "cloudy" is 0.7 requires developing a method to combine the two probabilities to

arrive at the required one.

Another question that begs to be answered is "how does one know the probabilities

in the first place?". There are two ways of computing the probabilities. The traditional

approach, called thefrequentist approach, bases the probability of an event on the

frequency of prior occurrences of the same event. Perhaps the simplest example is









computing the probability of getting "tails" in a fair-coin toss; the probability is based on

the number of times the coin landed on tails in an arbitrary number (say 100) of trials.

Clearly, the approach lacks applicability to many real world problems. The alternative is

to assign beliefvalues to the event, called the subjectivist or Bayesian4 approach,

"according to which probabilities encode degrees of belief about events in the world and

data are used to strengthen, update or weaken those degrees of belief. In this formalism,

degrees of belief are assigned to propositions (sentences that take on true or false values)

in some language, and those degrees of belief are combined and manipulated according to

the rules of probability calculus." (Pearl, 2000 (p.2)).

Two characteristics of belief values are worth noting. First, such values are

assigned based on some degree of belief the experimenter has in the occurrence of the

particular event and not on the frequency of the same. Second, they are governed by the

laws of probability. Using the second characteristic, experimenters change the degree of

belief assigned to different variables so that the assigned belief values are consistent with

the laws of probability. The next section explains the basic axioms of probability theory.

Subsequent sections build on the same laws and explain their application to BN.

2.5.2 Axioms of Probability

Probability calculus defines three basic axioms:

i. Probability of variable A being in state a, (denoted by P(A =a,)5 is a

number between 0 and 1. Thus,


4 After Reverend Thomas Bayes (more detail here)

5 As an example, consider the variable A that represents the probability of the car being of a certain color,
then the possible states of A are the possible colors of the car. If the possible colors (states) are red, blue,
green and white, then in order for the states to be mutually exclusive and exhaustive, the car has to have
one color and can never have more than one color.









0
and ZP(A=a,)=1


ii. P(A = a,) = 1 if and only if a, is certain.

iii. If A and B are two mutually exclusive events, then the probability

that either one or the other will occur is the sum of their individual

probabilities,

P(A=a, or B=bj) = P(A =a)+P(B=b,) --2.10

This is known as the additive rule or the theorem on the addition ofprobabilities.

2.5.3 Law of Total Probability

In contrast with the additive rule, joint probability of two events A and B is the

probability that both A andB will be in a given state at the same time. Joint probability of

independent events is the product of their individual probabilities. Therefore,

P(A = a,B = b, )= P(A = aj)P(B = b,) --2.11

Generalizing, probability of n independent events, E1 through En is given by


P(E1,...,E,,) = P(E) --2.12
1=1

For example, (A =a,B=b,) gives the joint probability of A=aj and B=b, (i.e., the

probability of A being in state a, and B in state b, simultaneously). P(A =a) and P(B=b,)

are known as the marginal probabilities of a, and b, respectively.

One implication of joint probability is the law of total probability. The law

provides a method to compute the marginalprobability of an event (say P(A =a)) given

the joint probability by summing over all the states of the other variable. Mathematically,









m
P(A = aj) = P(A = a,B = b,) --2.13


where m is the number of possible states of B.

The operation of summing over all values of b, is also called marginalizingg over

B". As an example, assume two fair coins, A and B and consider the question, "What is

the probability of getting "heads" on A?" The question can be answered by marginalizing

over B (i.e., summing over all the states of B in the joint probability of A and B). The

joint probability gives the probability of A and B being in some given state concurrently.

Let h represent getting "heads" and t represent "tails", so in this case, P(A = h, B =h)

represents the joint probability of getting "heads" in A and B simultaneously and P(A = h,

B =t) gives the joint probability of "heads" in A and "tails" in B. Adding the two joint

probabilities yields P(A=h),

P(A=h) = P(A = h, B =h) + P(A = h, B =t)

Or P(A h) = P(A= h,B= b,)


where b, are the possible states of B, in this case h and t.

From the above example it is clear that the marginal probability of any variable can

be computed by marginalizing (summing over all its states) over the variable in the joint

probability. This law forms the basis of probabilistic inference.

A corollary of this law is that the sum of the joint probabilities over all states of all

variables is 1,


Y-YP(A= aj,=b,) 1 --2.14
j=1 1=1

where n and m are the number of states of A and B respectively.









2.5.4 Conditional Probability

Two other concepts of probability calculus that play an important role in BN are

conditional probability and conditional independence of variables. This section deals

with the first of the two: Conditional probability gives the probability of an event given

the probability of another event.

P(A=a|B=b) = x --2.15

is read as the probability of A=a given the event B= b is x. Traditionally,

conditional probability is defined in terms of joint probability as


P(A B) (AB) --2.16
P(B)

The following example will be used throughout this section to explain application

of relationships to a real problem. The problem statement is to compute the probability of

the grass being wet (W) given the states of rain (R) and cloudiness (C). So the probability

of rain given cloudiness is

P(R,C)
P(R I C)- P(RC) --2.17
P(C)

This example will be referred to as the "wet grass" example in subsequent sections.

2.5.5 Chain Rule

According to Pearl (2000), the Bayesian approach to probability deems conditional

probability as a more basic relationship between variables than joint probability as it is

closer to the organization of human knowledge. Accordingly, equation (2.13) can be

written so as to compute the joint probability in terms of the conditional probabilities.

P(A,B) = P(A IB)P(B) --2.18









The above equation denotes the product over all the possible states of A and B. That

is, if A and B are dichotomous variables with states 0 and 1, the joint probability P(A,B) is

given by

P(A,B)= P(A = 0 B= 0)P(A = 01B = 1)P(A =1B = 0)P(A = 11B = 1)P(B = 0)P(B =1)


--2.19

This is known as the chain rule ofprobability and plays a critical role in BN.

Generalizing the chain rule to a set of n events E1,...,En, their joint probability is given by

the product of the conditional probabilities of each of the variables.

P(E,E2,...,E,) = P(E I E,_,...,E,E)... P(E2 I E,)P(E,)


or P(E, E2,..., E) = -P(E, I E 1,...,E2,E,) --2.20
J-1

The chain rule provides a method to compute the joint probability of all the

variables represented in a graphical model (BN). As an illustration, consider a variable

representing the state of a sprinkler (S) added to the wet grass example of the previous

section. The joint probability of all the variables is denoted as

P(W, S, R, C)= P(W S, R, C) P(S R, C) P(R I C) P(C)

2.5.6 Bayes' Theorem

Bayes' theorem provides method of updating belief in hypothesis B in light of

evidence A. Elaborating, equation (2.16) yields the following

P(A, B) = P(A I B) P(B) = P(B I A)P(A)

Rearranging these terms leads to the inversion formula, which is the heart of

Bayesian inference.









P(BIA)P(A)
P(A I B) = -- 2.21
P(B)

P(A B) is known as the posterior probability or posterior belief (Bayesian theorists

prefer using the term belief values rather than actual probability values to highlight the

notion that the values are not traditional probabilistic values) and is the product of the

prior belief (P(A)) and the likelihood of B given A (P(BIA) is the likelihood that B will

occur given that A is true) divided by a normalizing constant (P(B) can be obtained by

marginalizing as in equation (2.11)). The inversion formula (equation 2.19) and the chain

rule (equation 2.16) make it possible to compute the conditional probability of any

variable in a set of variables if the joint probability over the variables is known.

2.5.7 Conditional Independence

One problem with computing the joint probability distribution is the number of

computations required. As equation (2.17) illustrates, the number of terms required for

computing the joint probability increases exponentially with the number of variables;

conditional independence offers to reduce the number terms in many cases.

For two variables, A and B, if knowing the state of B does not affect the probability

of A, then A and B are said to be independent of each other; mathematically

P(AIB) = P(A) --2.22

Similarly, P(A B,C) = P(A C) implies that A and B are conditionally independent of

each other given C; that is, once C is known, knowing B does not change the belief value

of A. For example, in the wet grass example, the state of wetness of the grass is

conditionally independent of cloudiness given rain (i.e., given that it is raining, the

probability of cloudiness will not have any effect on the state of wetness of the grass).









Generalizing the relationship for a set E of n events {E1,...,En}, say there exists a set

pa,(E) consisting of variables E, is conditionally dependent upon, such that


P(E)= P(E,E2,...,E,) = -IP(EJ E, -,...,Ei) (from equation (2.20))
J-1

and,

P(E, I E|,,...,E,) = P(E I paj (E)) -- 2.23

Clearly, if the number of elements in paj(E) is less than n, it results in considerable

reduction in terms of computation required.

2.5.8 Graphical Notation

A brief review of graphical notation and concepts is necessary before further

discussion into BN. A graph G(VE) is a function of the set of vertices (V) and a set of

edges (E). Each edge is denoted by apair of vertices ((A,B) is an edge connecting the

vertices A and B) and may be directional (denoted by an arrowhead on one end) or

unidirectional (also called bi-directional, denoted by arrows on both ends or no arrows at

all). For bi-directional edges, (A,B) = (B,A) while the same is not true for directional

edges, which are denoted by an ordered pair of vertices, the first one denoting the

originating vertex for the edge and the second one denoting the terminating vertex. So

(A,B) denotes an edge starting at A and ending at B and (B,A) denotes one from B to A

and (A,B)(B,A). The vertex of origin is known as the parent of the ending vertex, which

is known as the child of the parent. A vertex may have multiple parents or multiple

children. Parents of parent nodes are known as ancestors; likewise all vertices descending

from any given node are known as its descendants. Two vertices with an edge between

them are called adjacent vertices. A path in a graph is a sequence of "connected" edges









(the terminating vertex of one edge is the originating vertex for the next, e.g.,

((A,B),(B,W),(W,E),(E,Z))). A directed path has all the edges pointing in the same

direction. Two edges in a graph are said to be connected if there exists a path between the

two edges (in the path listed in the previous example, A and Z are connected), else they

are disconnected. A path is called a cycle if it begins and ends on the same node (e.g.,

X->Y->X, distinct from self-loops, e.g., X->X). A graph is cyclic if it contains at least one

cycle. The same definition of cycles applies to both directed and undirected graphs. A

directed graph that does not contain any cycles is called a directed acyclic graph (DAG).

2.5.9 Causal Networks and d-separation

A causal network provides a method for reasoning under uncertainty by

constructing a graphical model that represents causal relationships between events

(Jensen, 2001). A directed graph represents the causal relationships, each elementary

variable in the problem forms a node (vertex) of the network and an edge from A to B can

be thought of as "A causes B". This property makes deciding the structure of graphical

models more intuitive as compared to other modeling techniques.

The d-separation criterion decides how evidence (probability of belief information)

is blocked from being transmitted from one node to another (Jensen, 2001) in a causal

network. Essentially, there are three types of connections in any directed graph; serial,

diverging and converging as illustrated in Figure 2.10 (a), (b) and (c) respectively.

Intuitively, it is easy to see that information can flow in serial (e.g., A= Cloudy, V=Rain,

B=Wet) and diverging (A=hair-length, V= Sex, B=Stature (Jensen, 2001)) connections

unless vertex Vis instantiated (has received some evidence). In situations depicted in

Figure 2.10 information can flow from A to B if and only if Vis not instantiated.









Specifically, in Figure 2.10 (a), knowing it is raining or not will negate any effect of

cloudiness on the state of wetness of grass and in Figure 2.10 (b) knowing the sex of a

person nullifies any effect knowledge of stature may have on hair-length and vice versa.

For converging connections however (e.g., A= Rain, B= Sprinkler, V=Pavement Wet and

D=Pavement slippery from Figure 2.10 (c)), information can flow only if the diverging

node or any of its descendants is instantiated. For the situation in Figure 2.10 (c),

information can travel from A to B if and only if Vor D is instantiated. (Jensen, 2001).

2.5.10 Bayesian Networks

Aprobabilistic model encodes information that allows computing probability of

any number of variables (propositions) represented in the model connected using

Boolean operators. As an example, the probabilistic model of the variables A, B and C

should allow computing the probability of all statements like A and B, (A and B)

or (not C), and so on. Each such term, formed by connecting the propositions using

Boolean operators, is called a well-formed sentence (Pearl, 2000) and is denoted by S.

Any joint distribution function (JDF) represents a complete probabilistic model

over the variables, since it allows computing the probability of any well-formed sentence.

The JDF is computed using the additive rule (equation 2.10) and using the following two

properties; (a) that every Boolean formula can be represented as a disjunction of

elementary events6 (Pearl, 2000), and (b) that elementary events are, by definition,

mutually exclusive. Conditional probabilities can be computed in a similar manner using

equation (2.16).



6 For example, A and B is the same as not (not A or not B). This is obtained from DeMorgan's theorem,
which states [NOT (A OR B) = A AND B] and[NOT(A AND B) = (NOT A) OR (NOT B) ].









By checking if sufficient information is available to compute the probability of

every elementary event in the function domain and if the probabilities sum up to 1, the

JDF can determine if sufficient information is available to specify a complete

probabilistic model and verify whether or not it is consistent with the data. If the model is

inconsistent, it specifies the additional information required and the points at which it is

required (Pearl, 2000). From the above discussion, it should be clear that deriving the

correct JDF for a given set of variables allows computing the probability of any well-

formed sentence (i.e., any combination of the variables). For most practical problems,

specifying joint probability functions depends on the problem domain; for continuous

variables, they are specified as algebraic expressions (like the normal distribution,

exponential distribution, etc.) while various indirect representation methods have been

developed for problems involving discrete variables. Graphical models are the most

promising of such indirect representations (Pearl, 2000).


A= Cloudy V Rain B= Wet

(a) O

A Hair
A Rain B= Sprinkler L J1
K- (b)


B=Stature


V=Wet
pavement





pavement









Figure 2.10 d-separation in (a)serial, (b) diverging and (c) converging connections.

Pearl (2000, p. 13) lists three advantages of using graphs in probabilistic and

statistical modeling:

1. they provide convenient means of expressing substantive assumptions;
2. they facilitate economical representation of joint probability functions; and
3. they facilitate efficient inferences from observations.

The second advantage is the most critical; as equation (2.17) illustrates, computing

the joint probability of two dichotomous variables requires four terms. Extending this,

computing the same for n variables requires 2n terms, making the entire calculation very

expensive computationally. Clearly, computational complexity can be reduced if each

term depends only on a small subset of the total terms. Graphical models help achieve

just such an economy.

Graphical models that use undirected graphs are referred to as Markov models

(Pearl, 1988) and are used mainly to represent symmetrical spatial relationships (Isham,

1981; Cox & Wermuth, 1996; Lauritzen, 1996). Directed graphical models, on the other

hand, employ directed graphs and are used to represent causal or temporal relationships

(Lauritzen, 1982; Wermuth & Lauritzen, 1983; Kiiveri et al, 1984) and are known as

Bayesian networks. "[BN are] so named to emphasize three aspects: (1) the subjective

nature of the input information; (2) the reliance on Bayes's conditioning as the basis for

updating information and; (3) a distinction between causal and evidential modes of

reasoning." (Pearl, 2000, p. 14). More formally, BN are graphical models with the

following properties (Jensen, 2001):

1. The graph of the models consists of a set of variables and a set of directed edges
between variables. The variables form the nodes of the graph and are connected by
directed edges. Each variable has a finite set of mutually exclusive states.