The Bayesian Structural EM Algorithm
This work addresses a key bottleneck in machine learning for researchers and practitioners dealing with missing data in probabilistic modeling, though it is incremental as it builds on prior Structural EM methods.
The paper tackles the problem of learning Bayesian network structures from incomplete data by extending the Structural EM algorithm to directly handle Bayesian model selection, proving its convergence and applying it to various probabilistic models.
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.