Probabilistic Graphical Models

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Generalizing Chow-LiuTree-augmented Naïve Bayes Model [Friedman ’97]If evidence variables are correlated, Naïve Bayesmodels can be overconfidentKey idea: Learn optimal tree for conditionaldistribution P(X 1 ,…,X n | Y)Can do optimally using Chow-Liu (homework! ☺)42
TasksSubscribe to Mailing listhttps://utils.its.caltech.edu/mailman/listinfo/cs155Select recitation timesRead Koller & Friedman Chapter 17.1-17.3, 18.1-2,18.4.1Form groups and think about class projects. If youhave difficulty finding a group, email Pete Trautman43
Page 1 and 2: ProbabilisticGraphical ModelsLectur
Page 3 and 4: Representing the world using BNss 1
Page 5 and 6: Additional conditional independenci
Page 7 and 8: Active trailsAn undirected path in
Page 9 and 10: Completeness of d-separationTheorem
Page 11 and 12: Representing the world using BNss 1
Page 13 and 14: Uniqueness of Minimal I-mapsIs the
Page 15 and 16: I-EquivalenceTwo graphs G, G’ are
Page 17 and 18: Immoralities and I-equivalenceA V-s
Page 19 and 20: Identifying the skeletonWhen is the
Page 21 and 22: Identifying immoralitiesWhen is X -
Page 23 and 24: Testing independenceSo far, assumed
Page 25 and 26: Parameter learningSuppose X is Bern
Page 27 and 28: Solving the optimization problem27
Page 29 and 30: Estimating CPDsGiven data D = {(x 1
Page 31 and 32: Algorithm for BN MLE31
Page 33 and 34: Structure learningTwo main classes
Page 35 and 36: Decomposable scoreLog-data likeliho
Page 37 and 38: Finding the optimal MLE structureOp
Page 39 and 40: Finding the optimal tree BNScoring
Page 41: Chow-Liu algorithmFor each pair X i

Probabilistic Graphical Models

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