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Induced semantics for undirected graphs: Another look at the Hammersley-Clifford theorem

Sears, Timothy; Sunehag, Peter


The Hammersley-Clifford (H-C) theorem relates the factorization properties of a probability distribution to the clique structure of an undirected graph. If a density factorizes according to the clique structure of an undirected graph, the theorem guarantees that the distribution satisfies the Markov property and vice versa. We show how to generalize the H-C theorem to different notions of decomposability and the corresponding generalized-Markov property. Finally we discuss how our technique...[Show more]

CollectionsANU Research Publications
Date published: 2007
Type: Book chapter
Book Title: Bayesian Inference and Maximum Entropy Methods in Science and Engineering
DOI: 10.1063/1.2821254


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