Mixtures of Polynomial With Tails as Probability Distributions: Theoretical and Experimental Evaluation

Abstract

Bayesian networks based on mixtures of polynomials (MoPs) are used to model multivariate hybrid or continuous probability distributions. MoPs provide a flexible yet simple model to deal with probabilistic reasoning, approximating complex or empirical probability distributions. We review the main models based on MoPs in the literature, introducing an alternative MoP approach: the mixtures of polynomials with tails (tMoPs). Also, we present procedures for learning tMoP marginal and conditional densities from data. This learning algorithms are tested with many well-known probability distributions. In these experiments, the tMoP models yield satisfactory results in comparison to other techniques, including other available MoPs alternatives. We also propose a meta-model that can directly, using interpolation, provide a tMoP expression for a specific density within a given family. This idea is tested with several probability distributions of one and two parameters, giving promising results.