Probabilistic Graphical Models - Caltech

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Learning general BNs Fully observable Missing data Known structure Easy! EM Unknown structure Hard (2.) Now 34
Structure learning with hidden data Fully observable case: Score(D;G) = likelihood of data under most likely parameters Decomposes over families Score(D;G) = ∑ ι FamScore i (X i | Pa Xi ) Can recompute score efficiently after adding/removing edges Incomplete data case: Score(D;G) = lower bound from EM Does not decompose over families Search is very expensive Structure-EM: Iterate Computing of expected counts Multiple iterations of structure search for fixed counts Guaranteed to monotonically improve likelihood score 35
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 and 24: Lower-bounding marginal likelihood
Page 25 and 26: M-step: Maximize lower bound Lower
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: Computing expected counts Suppose w
Page 37: Learning general BNs Fully observab

Probabilistic Graphical Models - Caltech

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