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We study the Bayesian model averaging approach to learning Bayesian networkstructures (DAGs) from data. We develop new algorithms including the firstalgorithm that is able to efficiently sample DAGs according to the exactstructure posterior. The DAG samples can then be used to construct estimatorsfor the posterior of any feature. We theoretically prove good properties of ourestimators and empirically show that our estimators considerably outperform theestimators from the previous state-of-the-art methods.

Structure Learning in Bayesian Networks of Moderate Size by Efficient Sampling