Bernal S D_2010.pdf - University of Plymouth

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4.5. FEEDBACK PROCESSING lihood functions A(x), the difference between the exact beliefs and the approximated beliefs obtained after sampling for different values of Nâx and kumax was measured. The difference was measured using the Kullback-Leibler (K-L) divergence. Figure 4.17 shows the K-L divergence between the real and approximate beliefs, averaged over 50 trials, as a function oiNâx and Kmax- ''or comparison, the K-L divergence between the exact belief and a randomly generated belief distribution is also plotted. The range over which these parameters are tested is limited by the computational cost associated with calculating the exact beliefs using CRTs of size exponential to the number of parents. Thus the chosen parameters are kx - 10. A,/ = 20,N = 6, A:„^^, - {I •• -19} and A/,„„. - {I - - -6}. The results show thai as A',^, and kumax increase, the goodness of hi between the approximation and the exact belief increases. Furthermore, the relative difference between the K-L divergence of the approximate and the random belief distributions suggests that even for relatively small values of vV„„, and jkumo^r the approximate belief provides agood fit to the exact belief. The sam pling parameters have lo be chosen as a compromise between the accuracy of the approximation and the computational cost. 181
4.5. {REDBACK PROCESSING true vs. random distributions (baseline) K Umax -*-Nmfl)(=1 -^l*nax = 3 — Nmax = 4 -^ Nma" = 5 - Nmaiê Random Figure4.!7: Kullback-l-eibler divergence between ihc true and the approximate prior function ;tfX) distribution for differeni values of kunmi and A',,, averaged over 50 trials. The Kullhack-l.eibler(K-l-) divergence, on ihcy-axis, measures the crosscorrelation hdiweun an approximult- disiribuliiin und the true dislribuiiuii, and is typically used as a goodness of fit between IwiMjiscreie probahilily distributions (Kri.ston and Kiehel 2()09, Winn and Bishop 2U()5, Hinton el al. 2()()f)). The xaxis .shows the number of samples taken from the K messages. k,„iu- Kesults are ploiled for values of N„a.i ranging from I to 6 as indicated in Ihc colour legend. The dolled hori/.onia! tine shows the K-l. divergence between ihe true and a random disirihuiion, which serves as a baseline to compare the goiHlness of lit of the approximate dislrihutions. 182 2D
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A cortical model of object percepti
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A cortical model of object percepti
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Contents Ab.stract V AcknowlcdRcnie
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4.7 Original contrihutions in this
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3.9 Example of belief propagation i
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5.19 SI and CI model responses to a
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XVI
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2009 Durabernal S. Wennekers T, Den
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J.I. OVERVIEW retinal stimulation (
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J.2. MAIN CONTRfBUTlONS • A revie
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2,1. OBJECT RECOGNITION ihe princip
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2.1. OBJECT REC(JGNmON The dorsal s
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2.1. OBJECT RECOGNJTION properties
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2.1. OBJECT RECOGNITION of input em
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2.1. OBJEOTRBCXiGNrnON ta) u I/I ^.
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2.1. OBJECT RECOGNITION 2.1.2.1 HMA
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2.1. OBJECT RECnCNmON unit will be
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2.1. OBJECT REC(X}NIT!ON tivity, st
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2.1. OBJECT RECOGNITION response fr
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2.2. HSGH-LEVEL FEEDBACK feature an
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2.2. HIGH-LEVEL FEEDBACK Thirdly, p
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2.2. mCH-LBVEL FEEDBACK Kandom 2 LO
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1.2. HIGH-LEVEL FEEDBACK « 70 U M
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2.2. HIGH-LEVEL FEEDBACK D Receptiv
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1.1. HIGH-LEVEL FEEDBACK context of
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2.2. HIGH-LEVEL FEEDBACK detailed i
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2.2. HIGH-LEVEL FEEDBACK activity g
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2.2. HIGH-LEVEL FEEDBACK task, such
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2.2. HIGH'lMîm,_WEDBACK 2004), and
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2.2. HIGH-LEVEL FEEDBACK However, t
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2.2. HIGH-LEVEL FEEDBACK sizes that
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2.3. ILLUSORY AND OCCLUDED CONTOURS
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2.3. a.LVSORY AND OCCLUDED CONTnURS
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2.4. ORIGINAL CONTRIBUTIONS IN THIS
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3.1. THE BAYBSIAN BRAIN HYPOTHESIS
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XI. THEBAYESIANBRAINHYPfmBSIS poste
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3.1. THE BAYESJAN BRAIN HYPOmESIS T
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3.2. EVIDENCE FROM THE BRAIN ity in
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3.3. DEFINITION AND MATHEMATlCACPOR
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3.3. DEFINITION AND MATHEMATICAL FO
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XX DEFINITION AND MATHEMATICAL FORM
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.1,3. DEHNITION AND MATHEMATICAL FO
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3 J. DEFINITION AND MATHEMATICAL FO
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3.3. DEFINITION AND MATHFMAnCAL FOR
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.1.3. DERNrnON AmMAnWMATtCAL FORMUL
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3.3. DEFINITION Am MATHEMATICAL FOR
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33. DEFINITION AND MATHEMATICAL FOR
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3.3. OmNmON AND MATHEMATSOALFORMVLA
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3.3. DEFlNmON AND MATHEMATICAL FORM
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3 J. DEFINITION AND MATHEMATICAL f-
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3.3. D^JmnON AND MATHEMATICAL F0RMU
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.1.3. DEFIânON AND MATHFMATICAL FO
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3.3. DEFINITION AND MATHEMATICAl. F
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3J. DEFINITION AND MATHEMATICAL FOR
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3.4. EXISTING MODELS is on models t
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.1.4. EXISTING MODELS Figure J. 10:
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3.4. EXISTING MODELS the node encod
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3.4. EXISTING MOOm^ Type of f>raph
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3.4. EXISTING MODELS The model comp
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X4. EXISTING MODELS ;v 1,1 gi (8>^8
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3A. EXISTING MODELS proposes a triv
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3.4. EXISTING MODELS by the higher
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Page 175 and 176: 4.3. LEARNING 4.3.2 S1-C1 CRTs The
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5.4. ORIGINAL CONTRIBUTIONS IN THIS
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6.1. ANALYSIS OF RESULTS dence and
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6.1. ANALYSIS OF RESULTS The graph
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6.t. ANALYSIS OF RESULTS used 10 co
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6.1. ANALYSIS OF RF.SULTS the image
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6.1. ANALYSIS OF RESULTS feedback w
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6.1. ANALYSIS OF RESULTS over lime.
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6.1. ANALYSIS OF RESULTS 6.1.2.5 Fe
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6.1. ANALYSIS Ot RESULTS step. Alth
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6.1. ANALYSIS OF RESULTS operations
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6.J. ANALYSIS OFRBSULTS model could
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6.1. ANALYSIS OF RESULTS Alternativ
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6.2. COMPARISON WITH EXPERIMENTAL B
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6.3. COMPARISON WITH PRKVIOUS MODBL
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6.4. FUTURE WORK to temporal contex
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6.5. CONCLUSIONS AND SUMMARY OF CON
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6.5. CONCLUSIONS AND SUMMARY OF CON
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• The HTM paliems correspond lo t
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Bolz, J.& Gilbert, CD. (1986), CJcn
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Friston, K. & Kiebel, S. (2009). 'C
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Hoffman. K. L. & Lngothetis, N K. (
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Lanyon. L. & Denham. S. (2(X)9), 'M
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Murray, M. M.. Wylie. G, R., Higgin
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Reynolds, J. H. &, Chelazzi, L. (20
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Stanley. D. A. & Rubin, N. (2003),
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