Bernal S D_2010.pdf - University of Plymouth

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3,3. i^^lNITION AND MATHEMATICAL FORMVLATION dition established by converging nodes, described in Section 3.3.2, and matches our intuition regarding multiple causes. Without any information about the state of the Waves, data on the slate of Gales should not influence the state of Moon, as they are conditionally independent causes. 3.3.3.10 Example of belief propagation with tree structure The previous examples are all based on a network with the same simple structure; a central node with two parents and two children node. Although this type of structure serves to demonstrate the main concepts behind belief propagation, it does not capture an inten2,sting effect of hê- stnictured networks, which is therefore described in this subsection. In this case the network has three levels organized in a tree structure as shown in Figure 3.9. In the first step, evidence propagates from two of the child nodes in the lower level, leading to the update of the belief in the intcnnediaie nodes. In the second step, the belief at the top level is updated, together with the belief of the lower-lever child nodes that hadn't been instantiated. The crucial process occurs in step three when a message is sent downward from the top node. Note this didn't happen in the network of the previous examples, where Ihe propagation ended once the message reached the top nodes. The reason is that in this case the top node receives messages from the two intermediate child nodes (the left and the right branches of the tree), and therefore it must generate a top-down message for each node convcyinp the evidence collected from the other node. In other words the evidence from the left branch must be propagated to the nodes in the right branch and vice versa. This is depicted graphically in steps three and four. In the original example, an equivalent flow of evidence would happen, for example, if node Gales had a second child node, such as Fallen frees. Evidence originating in the node Surfing would propagate up the node Waves to the root node Gales and back down the opposite branch. 'Caption for Figure 3.8. Cjtample of belief propagation wiih no evidence. When all the boltomup A messages received by a node show Hat ilistribuiions, as is ihe erase of node W, jnevKabiy all [he A messages sent to its parent nodes will also show flat distributions, regardless of the incoming n messages. The prior probability (or evidence) at Ihe top causal nodes 0 and M does not influence the other causal node, until their common child W gathers some diagnostic evidence. This reflects the d-separntion condiLioii established by converging nodes, described in Section 3.,^.2, and matches our intuition regarding multiple causes. Without iiny inlormaiiiin about the state of the Woven, data on the state of Gnies should not influence the stale of Moon, as they are conditionally independent causes, 103
3.3. DEFINITION AND MATHEMATICAL FORMULATION 1) 2) %J = fJ.JJ m' 10.51. ft«) Figure 3./i: For gaption see foolnDle-* 104 I Bs/(ml- • nfmj - (D.i, 0.5) 8e((mJ = iO.5,0.ij nfmj = fOJ, O.iJ SalfsJ = (0.
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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. ILLUSORY AND OCCLUDED CONTOURS
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Page 79 and 80: 2.3. a.LVSORY AND OCCLUDED CONTnURS
Page 81 and 82: 2.4. ORIGINAL CONTRIBUTIONS IN THIS
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Page 87 and 88: 3.1. THE BAYESJAN BRAIN HYPOmESIS T
Page 89 and 90: 3.2. EVIDENCE FROM THE BRAIN ity in
Page 91 and 92: 3.3. DEFINITION AND MATHEMATlCACPOR
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Page 95 and 96: XX DEFINITION AND MATHEMATICAL FORM
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Page 129 and 130: 3J. DEFINITION AND MATHEMATICAL FOR
Page 131 and 132: 3.4. EXISTING MODELS is on models t
Page 133 and 134: .1.4. EXISTING MODELS Figure J. 10:
Page 135 and 136: 3.4. EXISTING MODELS the node encod
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Page 139 and 140: 3.4. EXISTING MODELS The model comp
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Page 143 and 144: 3A. EXISTING MODELS proposes a triv
Page 145 and 146: 3.4. EXISTING MODELS by the higher
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Page 151 and 152: 3.4. EXISTING MODELS Fristonelal. 2
Page 153 and 154: 3.4. EXISTING MODELS Oulgoing teedl
Page 155 and 156: 3.5. ORIGINAL CONTRIBUTIONS IN THIS
Page 157 and 158: 4.1 HMAX AS A BAYESIAN NETWORK 4.1
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Page 167 and 168: 4.2. ARCHITECTURES 4.2 Architecture
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4.2. ARCmm^TVRES S3 I C2 s f S2 o o
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4.2. ARCHITECTURES S4 f C3 S3 I C2
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4.3. LEARNING 4.3.2 S1-C1 CRTs The
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4.3. LEARNING Weight matrix applied
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4.3. LEARNING CI group -1 •B •
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4.3. LEARNING 2. The list of select
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4.3. LEARNING node=«. Therefore, t
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4.3. LEARNING 4.3.4 S2-C2CPTS The w
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4.3. WARNING 60 S3 tealures (object
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4.4. FEEDFORWARD PROCESSING (he sim
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4.4. FEEDFORWARD PROCFSSING Figure
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4.5. FEEDBACK PROCESSING is proport
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4.5. F^mSACK PRCKESSING n^ (U,) i^(
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4.5. FEEDBACK PfiOCESSWG t.(VJ,) ji
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4.5. {REDBACK PROCESSING true vs. r
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4.5. FEEDBACK PROCES.SING 4.5.3.2 D
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4.5. FEEDBACK PROCESSING evidence i
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4.6. SUMMARY OF MODEL APPROXIMATION
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4.7. ORIGINAL CONTRIBUTIONS IN THIS
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5,1. FEEDFORWARD PROCESSING using t
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5.L FEEDFORWARD PROCESSING Slate =
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5.1. FEEDFORWARD PROCESSING 1^ Onem
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5.1. FEEDFORWARD PROCESSING j • H
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5.1. FEEDFORWARD PROCESSING 5.1.2 O
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5.1. FEEDFORWARD PROCESSING Normal
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5.1. FEEDFORWARD PROCESSING c g ra
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5-1. FEEDFORWARD PROCESSING 4 5 Non
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5.1. FEEDFORWARD PROCESSING 100 8 9
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S.i. FEEDFORWARD PnOCESSING 5.1.2.4
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5.2. FEEDBACK-MEDIATED ILLUSORY CON
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5.2. FEEDBACK MEDIATED ILLUSORY CON
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5.2. FEiiDBACK-MEDWTHD ILLUSORY CON
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5.2. FEEDBACK MEDIATED ILLUSORY CON
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5.2. FEEDBACK-MHDIATED ILLUSORY CON
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5.2. FEEDBACK'MEDIATED ILLUSORY CON
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5.2. FEEDBACK-MEDIATED ILLVSORY CON
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.5.2. FEEDBACK-MEDIATED ELUSORY CON
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5.2. FEEDBACK-MEDIATED SILUSORY CON
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5.2. FEEDBACK-MEDIATED ILLUSORY CON
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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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