Approximating Posterior Distributions in Belief Networks Using Mixtures

This paper derives an efficient algorithm for updating the mixture parameters and applies it to the problem of learning in sigmoid belief networks and demonstrates a systematic improvement over simple mean field theory as the number of mixture components is increased.

Abstract

Exact inference in densely connected Bayesian networks is computationally intractable, and so there is considerable interest in developing effective approximation schemes. One approach which has been adopted is to bound the log likelihood using a mean-field approximating distribution. While this leads to a tractable algorithm, the mean field distribution is assumed to be factorial and hence unimodal. In this paper we demonstrate the feasibility of using a richer class of approximating distributions based on mixtures of mean field distributions. We derive an efficient algorithm for updating the mixture parameters and apply it to the problem of learning in sigmoid belief networks. Our results demonstrate a systematic improvement over simple mean field theory as the number of mixture components is increased. 1 Introduction Bayesian belief networks can be regarded as a fully probabilistic interpretation of feedforward neural networks. Maximum likelihood learning for Bayesian n...