Conditional independence structures over four discrete random variables revisited: conditional Ingleton inequalities

Milan Studeny

doi:10.1109/tit.2021.3104250

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arXiv · 2012.04092

Conditional independence structures over four discrete random variables revisited: conditional Ingleton inequalities

Milan Studeny

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Abstract

The paper deals with conditional linear information inequalities valid for entropy functions induced by discrete random variables. Specifically, the so-called conditional Ingleton inequalities are in the center of interest: these are valid under conditional independence assumptions on the inducing random variables. We discuss five inequalities of this particular type, four of which has appeared earlier in the literature. Besides the proof of the new fifth inequality, simpler proofs of (some of) former inequalities are presented. These five information inequalities are used to characterize all conditional independence structures induced by four discrete random variables.

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Milan Studeny. 2020-12-07. Conditional independence structures over four discrete random variables revisited: conditional Ingleton inequalities. https://doi.org/10.1109/tit.2021.3104250

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