approximate inference - Caltech

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How many samples do we need? ! Hoeffding inequality Suppose f is bounded in [0,C]. Then ! Thus, probability of error decreases exponen)ally in N! ! Need to be able to draw samples from P 22
Sampling from a Bernoulli distribu)on ! Most random number generators produce (<strong>approximate</strong>ly) uniformly distributed random numbers ! How can we draw samples from X ~ Bernoulli(p)? 23
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 and 20: Sampling based inference ! So fa
Page 21: Sample approxima)ons of expecta)
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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