Generalized belief propagation for approximate inference in hybrid Bayesian networks

Abstract

We apply generalized belief propagation to approximate inference in hybrid Bayesian networks. In essence, in the algorithms developed for discrete networks we only have to change "strong marginalization" (exact) into "weak marginalization" (same moments) or, equivalently, the "sum" operation in the (generalized) sum-product algorithm into a "collapse" operation. We describe both a message-free single-loop algorithm based on fixed-point iteration and a more tedious double-loop algorithm guaranteed to converge to a minimum of the Kikuchi free energy.