Approximating probability density functions with mixtures of truncated exponentials

Mixtures of truncated exponentials (MTE) potentials are an alternative to discretization and Monte Carlo methods for solving hybrid Bayesian networks. Any probability density function (PDF) can be approximated by an MTE potential, which can always be 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 MTE potentials that approximate standard PDF’s and applications of these potentials for solving inference problems in hybrid Bayesian networks. These approximations will extend the types of inference problems that can be modeled with Bayesian networks, as demonstrated using three examples