From conditional independences to factorization constraints with discrete random variables. (English) Zbl 1001.68033

Malvestuto, F. M.

Ann. Math. Artif. Intell. 35, No. 1-4, 253-285 (2002).

Summary: 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.

MSC:

68P15

Database theory

Keywords:

chase computation; conditional independence; maximum-entropy principle; probabilistic reasoning