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Learning a Bayesian networks with bounded treewidth is important for reducingthe complexity of the inferences. We present a novel anytime algorithm (k-MAX)method for this task, which scales up to thousands of variables. Throughextensive experiments we show that it consistently yields higher-scoringstructures than its competitors on complete data sets. We then consider theproblem of structure learning from incomplete data sets. This can be addressedby structural EM, which however is computationally very demanding. We thusadopt the novel k-MAX algorithm in the maximization step of structural EM,obtaining an efficient computation of the expected sufficient statistics. Wetest the resulting structural EM method on the task of imputing missing data,comparing it against the state-of-the-art approach based on random forests. Ourapproach achieves the same imputation accuracy of the competitors, but in aboutone tenth of the time. Furthermore we show that it has worst-case complexitylinear in the input size, and that it is easily parallelizable.

Efficient Learning of Bounded-Treewidth Bayesian Networks from Complete and Incomplete Data Sets