Contribution of František Matúš to the research on conditional independence

0535808 - ÚTIA 2021 RIV CZ eng J - Journal Article
Studený, Milan
Contribution of František Matúš to the research on conditional independence.
Kybernetika. Roč. 56, č. 5 (2020), s. 850-874. ISSN 0023-5954
R&D Projects: GA ČR(CZ) GA19-04579S
Institutional support: RVO:67985556
Keywords : conditional independence * matroid * polymatroid * entropy function * semigraphoid * semimatroid
OECD category: Pure mathematics
Impact factor: 0.892, year: 2020
Method of publishing: Open access
http://library.utia.cas.cz/separaty/2020/MTR/studeny-0535808.pdf https://www.kybernetika.cz/content/2020/5/850

An overview of results of F. 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.
Permanent Link: http://hdl.handle.net/11104/0314146