Abstract

We describe a heuristic method for learning mixtures of Bayesian Networks (MBNs) from possibly incomplete data. The considered class of models is mixtures in which each mixture component is a Bayesian network encoding a conditional Gaussian distribution over a fixed set of variables. Some variables may be hidden or otherwise have missing observations. A key idea in our approach is to treat expected data as real data. This allows us to interleave structure and parameter search and to take advantage of closed form approximations for marginal likelihood. In addition, by treating expected data as real data, the search criterion factors by variable, making the search processes more efficient. We evaluate our approach on synthetic and real-world data sets. Keywords : Mixture models, Bayesian networks, structure learning, parameter learning, hidden variables, EM algorithm. 1 Introduction There is growing interest in a class of models for density estimation known as Bayesian networks. In the...

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