On Approximating Multidimensional Probability Distributions by Compositional Models

Because of computational problems, multidimensional probability distributions must be approximated by distributions which can be defined by a reasonable number of parameters. As a rule, distributions with a special dependence structure (i.e., complying with a system of conditional independence relations) are considered; graphical Markov models and especially Bayesian networks are often used. This paper proposes application of compositional models for this puropose. In addition to a theoretical background, a heuristic algorithm solving one part of a model learning process is presented. Its basic idea, construction of an approximation exploiting informational content of given low-dimensional distributions in a maximal possible way, was proposed by Albert Perez as early as in 1977