Part of Advances in Neural Information Processing Systems 10 (NIPS 1997)
Christopher M. Bishop, Neil D. Lawrence, Tommi Jaakkola, Michael I. Jordan
Exact inference in densely connected Bayesian networks is computation(cid:173) ally intractable, and so there is considerable interest in developing effec(cid:173) tive 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 as(cid:173) sumed 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 learn(cid:173) ing in sigmoid belief networks. Our results demonstrate a systematic improvement over simple mean field theory as the number of mixture components is increased.