General Gibbs Distribution

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Presentation transcript:

General Gibbs Distribution Representation Probabilistic Graphical Models Markov Networks General Gibbs Distribution

A D B C

Consider a fully connected pairwise Markov network over X1,…,Xn where each Xi has d values. How many parameters does the network have? O(dn) O(nd) O(n2d2) O(nd)

Gibbs Distribution Parameters: a1 b1 c1 0.25 c2 0.35 b2 0.08 0.16 a2 0.05 0.07 a3 0.15 0.21 0.09 0.18 Parameters:

Gibbs Distribution

Induced Markov Network

Which Gibbs distribution corresponds to the graph H? All of the above

Graph Structure & Factorization Factorization not unique, but same independencies

Summary Gibbs distribution represents distribution as a product of factors Induced Markov network connects every pair of nodes that are in the same factor Markov network structure doesn’t fully specify the factorization of P