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.

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.

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.

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 tobe 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 insigmoid belief networks. Our results demonstrate a systematic improvement over simple mean field theory as the number of mixture components is increased.