A. Perez, M. Studeny: Comparison of two methods for approximation of probability distributions with prescribed marginals. Kybernetika 43 (2007), n. 5, pp. 591-618.

Abstract
Let P be a discrete multidimensional probability distribution over a finite set of variables N which is only partially specified by the requirement that it has prescribed given marginals for A in S, where S is a class of subsets of N whose union is N. The paper deals with the problem of approximating P on the basis of those given marginals. The divergence of an approximation P' from P is measured by the relative entropy of P with respect to P'. Two methods for approximating P are compared. One of them uses formerly introduced concept of dependence structure simplification. The other one is based on an explicit expression, which has to be normalized. We give examples showing that neither of these two methods is universally better than the other. If one of the considered approximations P' really has the prescribed marginals then it appears to be the distribution P with minimal possible multiinformation. A simple condition on the class S implying the existence of an approximation P' with prescribed marginals is recalled. If the condition holds then both methods for approximating P give the same result.

AMS classification 68T30

Keywords
marginal problem,
relative entropy,
explicit expression,
dependence structure simplification,
multiinformation,
decomposable model,
asteroid

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