Unified Conditional Probability Density functions for hybrid Bayesian networks

Bayesian Network is a significant graphical model that is used to do probabilistic inference and reasoning under uncertainty circumstances. In many applications, existence of discrete and continuous variables in the model are inevitable which has lead to high amount of researches on hybrid Bayesian networks in the recent years. Nevertheless, one of the challenges in inference in hybrid BNs is the difference between conditional probability density functions of different types of variables. In this paper, we propose an approach to construct a Unified Conditional Probability Density function (UCPD) that can represent probability distribution for both types of variables. No limitation is considered in the topology of the network. Hence, the construction of the unified CPD is developed for all pairs of nodes. We take use from mixture of Gaussians in the UCPD construct. Additionally, we utilize Kullback-Liebler divergence to measure the accuracy of our estimations.