Inference in hybrid Bayesian networks with mixtures of truncated exponentials

Mixtures of truncated exponentials (MTE) potentials are an alternative to discretization for solving hybrid Bayesian networks. Any probability density function can be approximated with an MTE potential, which can always by marginalized in closed form. This allows propagation to be done exactly using the Shenoy-Shafer architecture for computing marginals, with no restrictions on the construction of a join tree. This paper presents a 4-piece MTE potential that approximates an arbitrary normal probability density function with any mean and a positive variance. The properties of this MTE potential are presented, along with examples that demonstrate its use in solving hybrid Bayesian networks. Assuming that the joint density exists, MTE potentials can be used for inference in hybrid Bayesian networks that do not fit the restrictive assumptions of the conditional linear Gaussian (CLG) model, such as networks containing discrete nodes with continuous parents.

• Type: Journal
• Year: 2006
• Where: IJAR
• Authors: Barry R. Cobb, Prakash P. Shenoy
• Keywords: Hybrid Bayesian Networks, IJAR 2006, MTE Potentials, Probability Density Function