On the Intersection and Composition properties of conditional independence

Fuente: arXiv
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Main Author: Boege, Tobias
Format: Preprint
Published: 2025
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author Boege, Tobias
author_facet Boege, Tobias
contents Compositional graphoids are fundamental discrete structures which appear in probabilistic reasoning, particularly in the area of graphical models. They are semigraphoids which satisfy the Intersection and Composition properties. These important properties, however, are not enjoyed by general probability distributions. This paper surveys what is known about them, providing systematic constructions of examples and counterexamples as well as necessary and sufficient conditions. Novel sufficient conditions for both properties are derived in the context of discrete random variables via information-theoretic tools.
format Preprint
id arxiv_https___arxiv_org_abs_2504_11978
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On the Intersection and Composition properties of conditional independence
Boege, Tobias
Information Theory
Statistics Theory
94A15 (primary) 62R01, 94A17 (secondary)
Compositional graphoids are fundamental discrete structures which appear in probabilistic reasoning, particularly in the area of graphical models. They are semigraphoids which satisfy the Intersection and Composition properties. These important properties, however, are not enjoyed by general probability distributions. This paper surveys what is known about them, providing systematic constructions of examples and counterexamples as well as necessary and sufficient conditions. Novel sufficient conditions for both properties are derived in the context of discrete random variables via information-theoretic tools.
title On the Intersection and Composition properties of conditional independence
topic Information Theory
Statistics Theory
94A15 (primary) 62R01, 94A17 (secondary)
url https://arxiv.org/abs/2504.11978