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

Timothy D. Sears; Peter Sunehag

doi:10.1063/1.2821254

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

Timothy D. Sears, Peter Sunehag

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › peer-review

2 Citations (Scopus)

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.

Original language	English
Title of host publication	Bayesian Inference and Maximum Entropy Methods in Science and Engineering - 27th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2007
Pages	125-132
Number of pages	8
DOIs	https://doi.org/10.1063/1.2821254
Publication status	Published - 2007
Event	27th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2007 - Saratoga Springs, NY, United States Duration: 8 Jul 2007 → 13 Jul 2007

Publication series

Name	AIP Conference Proceedings
Volume	954
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	27th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2007
Country/Territory	United States
City	Saratoga Springs, NY
Period	8/07/07 → 13/07/07

Access to Document

10.1063/1.2821254

Cite this

Sears, T. D., & Sunehag, P. (2007). Induced semantics for undirected graphs: Another look at the Hammersley-Clifford theorem. In Bayesian Inference and Maximum Entropy Methods in Science and Engineering - 27th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2007 (pp. 125-132). (AIP Conference Proceedings; Vol. 954). https://doi.org/10.1063/1.2821254

Sears, Timothy D. ; Sunehag, Peter. / Induced semantics for undirected graphs : Another look at the Hammersley-Clifford theorem. Bayesian Inference and Maximum Entropy Methods in Science and Engineering - 27th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2007. 2007. pp. 125-132 (AIP Conference Proceedings).

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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.",

keywords = "Graphical models, Hammersley-Clifford theorem, Tsallis statistics",

author = "Sears, {Timothy D.} and Peter Sunehag",

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note = "27th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2007 ; Conference date: 08-07-2007 Through 13-07-2007",

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Sears, TD & Sunehag, P 2007, Induced semantics for undirected graphs: Another look at the Hammersley-Clifford theorem. in Bayesian Inference and Maximum Entropy Methods in Science and Engineering - 27th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2007. AIP Conference Proceedings, vol. 954, pp. 125-132, 27th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2007, Saratoga Springs, NY, United States, 8/07/07. https://doi.org/10.1063/1.2821254

Induced semantics for undirected graphs: Another look at the Hammersley-Clifford theorem. / Sears, Timothy D.; Sunehag, Peter.
Bayesian Inference and Maximum Entropy Methods in Science and Engineering - 27th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2007. 2007. p. 125-132 (AIP Conference Proceedings; Vol. 954).

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › peer-review

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N2 - 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.

AB - 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.

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KW - Tsallis statistics

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Sears TD, Sunehag P. Induced semantics for undirected graphs: Another look at the Hammersley-Clifford theorem. In Bayesian Inference and Maximum Entropy Methods in Science and Engineering - 27th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2007. 2007. p. 125-132. (AIP Conference Proceedings). doi: 10.1063/1.2821254

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

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