We consider the problem of learning Bayesian networks (BNs) from complete discrete data. This problem of discrete optimisation is formulated as an integer program (IP). We describe the various steps we have taken to allow efficient solving of this IP. These are (i) efficient search for cutting planes, (ii) a fast greedy algorithm to find high-scoring (perhaps not optimal) BNs and (iii) tightening the linear relaxation of the IP. After relating this BN learning problem to set covering and the multidimensional 0-1 knapsack problem, we present our empirical results. These show improvements, sometimes dramatic, over earlier results.
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