Affiliation:
1. Department of Computer Science, Sapienza University of Rome, Via Salaria 113, 00198 Roma, Italy
Abstract
We introduce a new notion of convexity in digraphs, which we call incoming-path convexity, and prove that the incoming-path convexity space of a digraph is a convex geometry (that is, it satisfies the Minkowski–Krein–Milman property) if and only if the digraph is acyclic. Moreover, we prove that incoming-path convexity is adequate to characterize collapsibility of models generated by Bayesian networks. Based on these results, we also provide simple linear algorithms to solve two topical problems on Markov properties of a Bayesian network (that is, on conditional independences valid in a Bayesian network).
Publisher
World Scientific Pub Co Pte Lt
Subject
Discrete Mathematics and Combinatorics
Cited by
1 articles.
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