Learning naive Bayes regression models with missing data using mixtures of truncated exponentials

Abstract

In the last years, mixtures of truncated exponentials (MTEs) have received much attention within the context of probabilistic graphical models, as they provide a framework for hybrid Bayesian networks which is compatible with standard inference algorithms and no restriction on the structure of the network is considered. Recently, MTEs have also been successfully applied to regression problems in which the underlying network structure is a na ̈ıve Bayes or a TAN. However, the algorithms described so far in the literature operate over complete databases. In this paper we propose an iterative algorithm for constructing na ̈ıve Bayes regression models from incomplete databases. It is based on a variation of the data augmentation method in which the missing values of the explanatory variables are filled by simulating from their posterior distributions, while the missing values of the response variable are generated from its conditional expectation given the explanatory variables. We illustrate through a set of experiments with various databases that the proposed algorithm behaves reasonably well.