Geodesic
Contribution of František Matúš to the research on conditional independence
Kybernetika, Tome 56 (2020) no. 5, pp. 850-874

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An overview is given of results achieved by F. Matúš on probabilistic conditional independence (CI). 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 and his contribution to the theory of semigraphoids is mentioned as well. Finally, his results on the characterization of probabilistic CI structures induced by four discrete random variables and by four regular Gaussian random variables are recalled. Partial probabilistic representability by binary random variables is also mentioned.
DOI : 10.14736/kyb-2020-5-0850
Classification : 05B35, 62H05, 68T30
Keywords: conditional independence; matroid; polymatroid; entropy function; semigraphoid; semimatroid 
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Studený, Milan. Contribution of František Matúš to the research on conditional independence. Kybernetika, Tome 56 (2020) no. 5, pp. 850-874. doi: 10.14736/kyb-2020-5-0850

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