M. Studeny: Conditional independence structures over four discrete random variables revisited: conditional Ingleton inequalities. IEEE Transactions on Information Theory 67 (2021), n. 11, pp. 7030-7049.

The paper deals with 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.

AMS classification 94A17 62B10 90C27 52B40 68T30

entropy function
discrete random variables
conditional information inequalities
conditional independence

A pdf version of a preprint (343kB) is available.

The paper builds on a number of publications by Frantisek Matus, chosen from: