Probabilistic Graphical Models

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Finding the optimal MLE structureLog-likelihood score:Want G * = argmax G Score(G ; D)Lemma: G ⊆ G’ Score(G; D) ≤ Score(G’; D)36
Finding the optimal MLE structureOptimal solution for MLE is always the fullyconnected graph!!! ☹Non-compact representation; Overfitting!!Solutions:Priors over parameters / structures (later)Constraint optimization (e.g., bound #parents)37
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: Decomposable scoreLog-data likeliho
Page 39 and 40: Finding the optimal tree BNScoring
Page 41 and 42: Chow-Liu algorithmFor each pair X i
Page 43: TasksSubscribe to Mailing listhttps

Probabilistic Graphical Models

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