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

Citation

Source

Type

Book chapter

Book Title

Bayesian Inference and Maximum Entropy Methods in Science and Engineering

Entity type

Access Statement

License Rights

Restricted until

2037-12-31
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