Induced semantics for undirected graphs: Another look at the Hammersley-Clifford theorem
Date
2007
Authors
Sears, Timothy
Sunehag, Peter
Journal Title
Journal ISSN
Volume Title
Publisher
American Institute of Physics (AIP)
Abstract
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 might be used to arrive at other generalizations of the H-C theorem, inducing a graph semantics adapted to the modeling problem.
Description
Keywords
Keywords: Graphical models; Hammersley-Clifford theorem; Tsallis statistics
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Source
Type
Book chapter
Book Title
Bayesian Inference and Maximum Entropy Methods in Science and Engineering
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Restricted until
2037-12-31