approximate inference - Caltech

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Does Loopy BP always converge? ! No! Can oscillate! ! Typically, oscilla)on the more severe the more “determinis)c” the poten)als Graphs from K. Murphy UAI ‘99 16
What about MPE queries? ! E.g.,: What’s the most likely assignment to the unobserved variables, given the observed ones? E B A J M ! Use max-‐product (same as sum-‐product/BP, but with max instead of sums!) 17
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 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: Behavior of Loopy BP X 1 1 True
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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