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On factorization of probability distributions over directed graphs
Kybernetika, Tome 34 (1998) no. 1, pp. 57-68 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Four notions of factorizability over arbitrary directed graphs are examined. For acyclic graphs they coincide and are identical with the usual factorization of probability distributions in Markov models. Relations between the factorizations over circuits are described in detail including nontrivial counterexamples. Restrictions on the cardinality of state spaces cause that a factorizability with respect to some special cyclic graphs implies the factorizability with respect to their, more simple, strict edge-subgraphs. This gives sometimes the possibility to break circuits and get back to the acyclic, well-understood case.
Four notions of factorizability over arbitrary directed graphs are examined. For acyclic graphs they coincide and are identical with the usual factorization of probability distributions in Markov models. Relations between the factorizations over circuits are described in detail including nontrivial counterexamples. Restrictions on the cardinality of state spaces cause that a factorizability with respect to some special cyclic graphs implies the factorizability with respect to their, more simple, strict edge-subgraphs. This gives sometimes the possibility to break circuits and get back to the acyclic, well-understood case.
Classification : 05C20, 60B15, 62H99, 68T30
Keywords: factorizability; directed graph 
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Matúš, František; Strohmeier, Bernhard. On factorization of probability distributions over directed graphs. Kybernetika, Tome 34 (1998) no. 1, pp. 57-68. http://geodesic.mathdoc.fr/item/KYB_1998_34_1_a5/

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