Abstract
Factorization constraints are introduced as a generalization of the multiplicative formulation of conditional independence, and some computational and logic properties are stated. More precisely, we prove that factorization constraints characterize those cases in which a probability distribution can be represented “without loss of information” by a suitable set of its marginals. Moreover, we provide a sound formal system for factorization constraints, which covers the set of the so-called semi-graphoid axioms of conditional independence. Finally, we solve the implication problem for factorization constraints in two special cases, and for the general case we state two conditions, one necessary and the other sufficient for an implication to hold.
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Malvestuto, F. From Conditional Independences to Factorization Constraints with Discrete Random Variables. Annals of Mathematics and Artificial Intelligence 35, 253–285 (2002). https://doi.org/10.1023/A:1014551721406
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DOI: https://doi.org/10.1023/A:1014551721406