F. Matus and M. Studeny: Conditional independences among four random variables I. Combinatorics, Probability and Computing 4 (1995), n. 3, pp. 267-278.

The conditional independence structures within a system of four discrete random variables are studied. The problem which structures can occur is transformed into an analysis of a certain cone of set functions, namely polymatroids. Then, the cone is decomposed into two parts with help of Ingleton's inequalities. The first part is completely solved by giving the list of generating examples and the second part is strongly reduced.

The problem above was later completely solved in the subsequent series of papers by Frantisek Matus.

AMS classification 62H05, 52B40

conditional independence
functional dependence
Ingleton's inequality
Shannon entropy

Here is the whole series of papers by Frantisek Matus: