Tightening Bounds for Bayesian Network Structure Learning

A recent breadth-first branch and bound algorithm (BFBnB) for learning Bayesian network structures (Malone et al. 2011) uses two bounds to prune the search space for better efficiency; one is a lower bound calculated from pattern database heuristics, and the other is an upper bound obtained by a hill climbing search. Whenever the lower bound of a search path exceeds the upper bound, the path is guaranteed to lead to suboptimal solutions and is discarded immediately. This paper introduces methods for tightening the bounds. The lower bound is tightened by using more informed variable groupings when creating the pattern databases, and the upper bound is tightened using an anytime learning algorithm. Empirical results show that these bounds improve the efficiency of Bayesian network learning by two to three orders of magnitude.