Marginalizing in undirected graph and hypergraph models

Authors:
Enrique F. Castillo;Juan Ferrándiz;Pilar Sanmartín
Affiliations:
Dept. of Applied Mathematics and Computational Sciences, University of Cantabria, Santander, Spain;Department of Statistics and Operations Research, University of Valencia, Spain;Department of Mathematics, Jaume I University, Castellón, Spain
Venue:
UAI'98 Proceedings of the Fourteenth conference on Uncertainty in artificial intelligence
Year:
1998

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Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs

SIAM Journal on Computing
Expert Systems and Probabiistic Network Models

Expert Systems and Probabiistic Network Models

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Abstract

Given an undirected graph G or hypergraph H model for a given set of variables V, we introduce two marginalization operators for obtaining the undirected graph GA or hypergraph HA associated with a given subset A ⊂ V such that the marginal distribution of A factorizes according to GA or HA, respectively. Finally, we illustrate the method by its application to some practical examples. With them we show that hypergraph models allow defining a finer factorization or performing a more precise conditional independence analysis than undirected graph models.