Contribution of František Matúš to the research on conditional independence

Milan Studený

Kybernetika (2020)

  • Volume: 56, Issue: 5, page 850-874
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Studený, Milan. "Contribution of František Matúš to the research on conditional independence." Kybernetika 56.5 (2020): 850-874. <http://eudml.org/doc/297185>.

@article{Studený2020,
abstract = {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.},
author = {Studený, Milan},
journal = {Kybernetika},
keywords = {conditional independence; matroid; polymatroid; entropy function; semigraphoid; semimatroid},
language = {eng},
number = {5},
pages = {850-874},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Contribution of František Matúš to the research on conditional independence},
url = {http://eudml.org/doc/297185},
volume = {56},
year = {2020},
}

TY - JOUR
AU - Studený, Milan
TI - Contribution of František Matúš to the research on conditional independence
JO - Kybernetika
PY - 2020
PB - Institute of Information Theory and Automation AS CR
VL - 56
IS - 5
SP - 850
EP - 874
AB - 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.
LA - eng
KW - conditional independence; matroid; polymatroid; entropy function; semigraphoid; semimatroid
UR - http://eudml.org/doc/297185
ER -

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