Inference in hybrid Bayesian networks using mixtures of polynomials
The main goal of this paper is to describe inference in hybrid Bayesian networks (BNs) using mixture of polynomials (MOP) approximations of probability density functions (PDFs). Hybrid BNs contain a mix of discrete, continuous, and conditionally deterministic random variables. The conditionals for continuous variables are typically described by conditional PDFs. A major hurdle in making inference in hybrid BNs is marginalization of continuous variables, which involves integrating combinations of conditional PDFs. In this paper, we suggest the use of MOP approximations of PDFs, which are similar in spirit to using mixtures of truncated exponentials (MTEs) approximations. MOP functions can be easily integrated, and are closed under combination and marginalization. This enables us to propagate MOP potentials in the extended Shenoy-Shafer architecture for inference in hybrid BNs that can include deterministic variables. MOP approximations have several advantages over MTE approximations of PDFs. They are easier to find, even for multidimensional conditional PDFs, and are applicable for a larger class of deterministic functions in hybrid BNs.(C) 2010 Elsevier Inc. All rights reserved.
inference in hybrid bayesian networks hybrid bayesian networks mixtures of polynomials mixtures of truncated exponentials extended shenoy-shafer architecture shenoy-shafer architecture