Abstract

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 is then completely solved in the following papers:

• F. Matus: Conditional independences among four random variables II. Combinatorics, Probability and Computing 4 (1995), n. 4, pp. 407-417.
• F. Matus: Conditional independences among four random variables III. Submited to Combinatorics, Probability and Computing.

AMS classification 62H05, 52B40

Keywords

conditional independence

functional dependence

polymatroid

Ingleton's inequality

Shannon entropy

You may either download ps versions of these papers from here below or contact Frantisek Matus at matus@utia.cas.cz (for Matus's home page of click here):

F. Matus and M. Studeny (1995) Conditional independences among four random variables I. Combinatorics, Probability & Computing 4 269-278.

F. Matus (1995) Conditional independences among four random variables II. Combinatorics, Probability & Computing 4 407-417.

F. Matus (1999) Conditional independences among four random variables III: final conclusion. Combinatorics, Probability & Computing 8 269-276.