  In recent years there has been a flurry of works on learning Bayesian
networks from data. One of the hard problems in this area is how to effectively
learn the structure of a belief network from incomplete data- that is, in the
presence of missing values or hidden variables. In a recent paper, I introduced
an algorithm called Structural EM that combines the standard Expectation
Maximization (EM) algorithm, which optimizes parameters, with structure search
for model selection. That algorithm learns networks based on penalized
likelihood scores, which include the BIC/MDL score and various approximations
to the Bayesian score. In this paper, I extend Structural EM to deal directly
with Bayesian model selection. I prove the convergence of the resulting
algorithm and show how to apply it for learning a large class of probabilistic
models, including Bayesian networks and some variants thereof.
