Advances in Bayesian Network Learning using Integer Programming
  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.
