Probabilistic Graphical Models - Caltech

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Lower bound on marginal likelihood Bound of marginal likelihood with hidden variables Recall: Likelihood in fully observable case: Lower-bound interpreted as “weighted” data set 24
M-step: Maximize lower bound Lower bound: Choose θ (t+1) to maximize lower bound Use expected sufficient statistics (counts). Will see: Whenever we used Count(x,z) in fully observable case, replace by E Q t+1[Count(x,z)] 25
Page 1 and 2: Probabilistic Graphical Models Lect
Page 3 and 4: Approximate inference Three major c
Page 5 and 6: Monte Carlo sampling from a BN Sort
Page 7 and 8: Sampling from intractable distribut
Page 9 and 10: Designing Markov Chains 1) Proposal
Page 11 and 12: Summary of Sampling Randomized appr
Page 13 and 14: Assumed Recall: The “light” sid
Page 15 and 16: Remaining Challenges Inference Appr
Page 17 and 18: Dealing with missing data So far, h
Page 19 and 20: Learning with missing data Suppose
Page 21 and 22: E-Step: x: observed data; z: hidden
Page 23: Lower-bounding marginal likelihood
Page 27 and 28: EM for Gaussian Mixtures 27
Page 29 and 30: EM in Bayes Nets Complete data like
Page 31 and 32: Need to compute E-Step for BNs For
Page 33 and 34: Computing expected counts Suppose w
Page 35 and 36: Structure learning with hidden data
Page 37: Learning general BNs Fully observab

Probabilistic Graphical Models - Caltech

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