Machine Learning of Bayesian Networks Using Constraint Programming

Bayesian networks are a widely used graphical model with diverse applications in knowledge discovery, classification, prediction, and control. Learning a Bayesian network from discrete data can be cast as a combinatorial optimization problem and there has been much previous work on applying optimization techniques including proposals based on ILP, A* search, depth-first branch-and-bound (BnB) search, and breadth-first BnB search. In this paper, we present a constraint-based depth-first BnB approach for solving the Bayesian network learning problem. We propose an improved constraint model that includes powerful dominance constraints, symmetry-breaking constraints, cost-based pruning rules, and an acyclicity constraint for effectively pruning the search for a minimum cost solution to the model. We experimentally evaluated our approach on a representative suite of benchmark data. Our empirical results compare favorably to the best previous approaches, both in terms of number of instances solved within specified resource bounds and in terms of solution time.