0535808 20240903170647.020201208235959.9 000596316600002 85100175531 10.14736/kyb-2020-5-0850 25 s. P cav_un_epca*02971630023-5954565 (2020)850-874Ústav teorie informace a automatizace AV ČR, v. v. i. conditional independence matroid polymatroid entropy function semigraphoid semimatroid cav_un_auth*0101202 Studený Milan UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2020/MTR/studeny-0535808.pdf https://www.kybernetika.cz/content/2020/5/850 GA19-04579S GA ČR CZ cav_un_auth*0380558 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. WOS BA 10000 10100 10101 2021 1 RVO:67985556 http://hdl.handle.net/11104/0314146 S 3+4 Article Computer Science Cybernetics A COMPUTERSCIENCE.CYBERNETICS 0.800 0.056 11.3 0.00083 0.262 903 43 0.218 32.88 0.95 181 Q3 0.808 54 Q4 14.97 10.9 Q4 Q4 0.15 Q4 10.87 2020 85100175531 SCOPUS PUBMED 000596316600002 WOS cav_un_epca*0297163 Kybernetika 0023-5954 Roč. 56 č. 5 2020 850 874 Ústav teorie informace a automatizace AV ČR, v. v. i.