Approximating conditional MTE distributions by means of mixed trees

Abstract

Mixtures of truncated exponential (MTE) distributions have been shown to be a powerful alternative to discretisation within the framework of Bayesian networks. One of the features of the MTE model is that standard propagation algorithms as Shenoy-Shafer and Lazy propagation can be used. Estimating conditional MTE densities from data is a rather difficult problem since, as far as we know, such densities cannot be expressed in parametric form in the general case. In the univariate case, regression-based estimators have been successfully employed. In this paper, we propose a method to estimate conditional MTE densities using mixed trees, which are graphical structures similar to classification trees. Criteria for selecting the variables during the construction of the tree and for pruning the leaves are defined in terms of the mean square error and entropy-like measures.