approximate inference - Caltech

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Factor graph ! A factor graph for a Bayesian network is a bipar)te graph consis)ng of ! Variables and ! Factors ! Each factor is associated with a subset of variables, and all CPDs of the Bayesian network have to be assigned to one of the factor nodes C D I f 1 f 2 f 3 f 4 CD DIG IGS SL G S L C D G I S L 10
Sum-‐product message passing on factor graphs ! Messages from node v to factor u ! Messages from factor u to node v f 1 f 2 f 3 f 4 CD DIG IGS SL C D G I S L 11
Page 1 and 2: Introduc)on to Ar)ficial Intellig
Page 3 and 4: Typical queries: Condi)onal dist
Page 5 and 6: Hardness of inference for gener
Page 7 and 8: Variable elimina)on algorithm ! G
Page 9: Factor graphs ! P(C,D,G,I,S,L) =
Page 13 and 14: Belief propaga)on on polytrees !
Page 15 and 16: Behavior of Loopy BP X 1 1 True
Page 17 and 18: What about MPE queries? ! E.g.,:
Page 19 and 20: Sampling based inference ! So fa
Page 21 and 22: Sample approxima)ons of expecta)
Page 23 and 24: Sampling from a Bernoulli distr
Page 25 and 26: Forward sampling from a BN 25
Page 27 and 28: Compu)ng probabili)es through sa
Page 29 and 30: Sample complexity for probabilit
Page 31: Gibbs sampling ! Start with ini)

approximate inference - Caltech

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