Probabilistic Graphical Models

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Finding the optimal tree skeletonCan reduce to following problem:Given graph G = (V,E), and nonnegative weights w e foreach edge e=(X i ,X j )In our case: w e = I(X i ,X j )Want to find tree T⊆ E that maximizes ∑ e∈T w eMaximum spanning tree problem!Can solve in time O(|E| log |E|)!40
Chow-Liu algorithmFor each pair X i , X j of variables computeCompute mutual informationDefine complete graph with weight of edge (X i ,X i )given by the mutual informationFind maximum spanning tree skeletonOrient the skeleton using breadth-first search41
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: Finding the optimal tree BNScoring
Page 43: TasksSubscribe to Mailing listhttps

Probabilistic Graphical Models

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