approximate inference - Caltech

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Compu)ng expecta)ons ! OQen, we’re not necessarily interested in compu)ng marginal distribu)ons, but certain expecta)ons: ! Moments (mean, variance, …) ! Event probabili)es 20
Sample approxima)ons of expecta)ons ! x 1 ,…,x N samples from RV X ! Law of large numbers: ! Hereby, the convergence is with probability 1 (almost sure convergence) ! Finite samples: 21
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 and 16: Behavior of Loopy BP X 1 1 True
Page 17 and 18: What about MPE queries? ! E.g.,:
Page 19: Sampling based inference ! So fa
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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