  For decomposable score-based structure learning of Bayesian networks,
existing approaches first compute a collection of candidate parent sets for
each variable and then optimize over this collection by choosing one parent set
for each variable without creating directed cycles while maximizing the total
score. We target the task of constructing the collection of candidate parent
sets when the score of choice is the Bayesian Information Criterion (BIC). We
provide new non-trivial results that can be used to prune the search space of
candidate parent sets of each node. We analyze how these new results relate to
previous ideas in the literature both theoretically and empirically. We show in
experiments with UCI data sets that gains can be significant. Since the new
pruning rules are easy to implement and have low computational costs, they can
be promptly integrated into all state-of-the-art methods for structure learning
of Bayesian networks.
