Abstract

An overview of results of Frantisek Matus on probabilistic conditional independence (CI) is given. First, his axiomatic characterizations of stochastic functional dependence and unconditional independence are recalled. Then his elegant proof of discrete probabilistic representability of a matroid based on its linear representability over a finite field is recalled. It is explained that this result was a basis of his methodology for constructing a probabilistic representation of a given abstract CI structure. His embedding of matroids into (augmented) abstract CI structures is recalled. The contribution of his to the theory of semigraphoids is mentioned, too. Finally, his results on the characterization of probabilistic CI structures induced by 4 discrete random variables and by 4 regular Gaussian random variables are recalled. Partial probabilistic representability by binary random variables is also mentioned.

AMS classification 62H05 05B35 68T30

Keywords

conditional independence

matroid

polymatroid

entropy function

semigraphoid

semimatroid

A pdf version of the published paper (413kB) is available.

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

• F. Matus: his home page at Institute of Information Theory and Automation, Prague.