An Algorithm for Inferences in a Polytree with Heterogeneous Conditional Distributions

This paper describes a general scheme for accomodating different types of conditional distributions in a Bayesian network. The algorithm is based on the polytree algorithm for Bayesian network inference, in which "messages " (probability distributions and likelihood functions) are computed. The posterior for a given variable depends on the messages sent to it by its parents and children, if any. In this scheme, an exact result is computed if such a result is known for the incoming messages, otherwise an approximation is computed, which is a mixture of Gaussians. The approximation may then be propagated to other variables. Approximations for likelihood functions (-messages) are not computed; the approximation step is put off until the likelihood function is combined with a probability distribution --- this avoids certain numerical difficulties. In contrast with standard polytree algorithms, which can only accomodate distributions of a few types at most, this heterogeneous polytree algor..