Learning mixtures of polynomials from data using B-spline interpolation

Hybrid Bayesian networks efficiently encode a joint probability distribution over a set of continuous and discrete variables. Several approaches have been recently proposed for working with hybrid Bayesian networks, e.g., mixtures of truncated basis functions, mixtures of truncated exponentials or mixtures of polynomials (MoPs). We present a method for learning MoP approximations of probability densities from data using a linear combination of B-splines. Maximum likelihood estimators of the mixing coefficients of the linear combination are computed, and model selection is performed using a penalized likelihood criterion, i.e., the BIC score. Artificial examples are used to analyze the behaviour of the method according to different criteria, like the quality of the approximations and the number of pieces in the MoP. Also, we study the use of the proposed method as anon-parametric density estimation technique in naive Bayes (NB) classifiers. Results on real datasets show that the non-parametric NB classifier using MoPs is comparable to the kernel density-based NB and better than Gaussian or discrete NB classifiers.