approximate inference - Caltech

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Inference ! Can exploit structure (condi)onal independence) to efficiently perform exact inference in many prac)cal situa)ons ! For BNs where exact inference is not possible, can use algorithms for approximate inference (later) 6
Variable elimina)on algorithm ! Given BN and Query P(X | E=e) ! Choose an ordering of X 1 ,…,X n ! Set up ini)al factors: f i = P(X i | Pa i ) ! For i =1:n, X i ∉ {X,E} ! Collect all factors f that include X i ! Generate new factor by marginalizing out X i ! Add g to set of factors ! Renormalize P(x,e) to get P(x | e) 7
Page 1 and 2: Introduc)on to Ar)ficial Intellig
Page 3 and 4: Typical queries: Condi)onal dist
Page 5: Hardness of inference for gener
Page 9 and 10: Factor graphs ! P(C,D,G,I,S,L) =
Page 11 and 12: Sum-‐product message passing
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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