Conditional independence structures over four discrete random variables revisited: conditional Ingleton inequalities
This work provides a complete characterization of conditional independence structures for four discrete random variables, which is an incremental step in information theory.
This paper revisits conditional Ingleton inequalities, which are linear information inequalities for entropy functions under conditional independence assumptions. It discusses five such inequalities, presenting a new fifth inequality and simpler proofs for some existing ones. These inequalities are then used to characterize all conditional independence structures induced by four discrete random variables.
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.