Prologue to Belief Propagation and its Generalizations.

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Prologue to Belief Propagation and its Generalizations. Max Welling Donald Bren School of Information and Computer and Science University of California Irvine

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Graphical Models A "marriage" between likelihood hypothesis and diagram hypothesis Why probabilities? Dissuading vulnerabilities, certainty levels Many procedures are intrinsically "loud" ��  strength issues Why charts? Give essential structure in substantial models: - Designing new probabilistic models. - Reading out (contingent) independencies. Deduction & advancement: - Dynamical programming - Belief Propagation

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Types of Graphical Model i Parents(i) j i Undirected chart (Markov arbitrary field) Directed diagram (Bayesian system) figure charts communications factors

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? air or water ? ? high data districts low data locales neighborhood data Example 1: Undirected Graph

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Undirected Graphs (cont'ed) Nodes encode shrouded data (fix character). They get nearby data from the picture (splendor, shading). Data is engendered however the chart over its edges. Edges encode "similarity" between hubs.

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Example 2: Directed Graphs … PCs TOPICS war creatures Iraqi the Matlab

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Inference in Graphical Models Inference: Answer questions about in secret arbitrary factors, given estimations of watched irregular factors. More broad: register their joint back appropriation: Why do we require it? Answer inquiries : - Given past buys, in what kind books is a customer intrigued? - Given an uproarious picture, what was the first picture? Taking in probabilistic models from cases ( desire amplification, iterative scaling ) Optimization issues: min-cut, max-stream, Viterbi, … learning deduction Example : P( = ocean | picture) ?

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Approximate Inference is computationally unmanageable for huge charts (with cycles). Estimated techniques: Markov Chain Monte Carlo examining. Mean field and more organized variational procedures. Conviction Propagation calculations.

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outer confirmation message Compatibilities (connections) conviction (rough minor likelihood ) Belief Propagation on trees k M ki i k j i k

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outside proof message Compatibilities (cooperations) conviction (estimated negligible likelihood ) Belief Propagation on loopy charts k M ki i k j i k

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Some certainties about BP is correct on trees. On the off chance that BP merges it has achieved a neighborhood least of a goal capacity (the Bethe free vitality Yedidia '00 , Heskes '02 ) ��  frequently great estimation If it focalizes, union is quick close to the altered point. Numerous energizing applications: - mistake rectifying translating ( MacKay, Yedidia, McEliece, Frey ) - vision ( Freeman, Weiss ) - bioinformatics ( Weiss ) - requirement fulfillment issues ( Dechter ) - diversion hypothesis ( Kearns ) - …

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BP Related Algorithms Convergent options (Welling,Teh'02, Yuille'02, Heskes'03) Expectation Propagation (Minka'01) Convex options (Wainwright'02, Wiegerinck,Heskes'02) Linear Response Propagation (Welling,Teh'02) Generalized Belief Propagation (Yedidia,Freeman,Weiss'01) Survey Propagation (Braunstein,Mezard,Weigt,Zecchina'03)

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Generalized Belief Propagation Idea: To figure the dissemination of one of your neighbors, you request that your different neighbors figure your appropriation. Sentiments get joined multiplicatively. GBP BP

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Marginal Consistency Solve surmising issue independently on every "fix", then fasten them together utilizing "peripheral consistency".

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Region Graphs (Yedidia, Freeman, Weiss '02) Stitching together arrangements on neighborhood bunches by upholding "peripheral consistency" on their convergences. C=1 C=… C=… C=… C=… C=… C=… C=… C=… C=… Region : accumulation of cooperations & factors.