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Bayesian network learning with cutting planes
James Cussens
Department of Computer Science, University of York
The problem of learning the structure of Bayesian networks from complete discrete data with a limit on parent set size is considered. Learning is cast explicitly as an optimisation problem where the goal is to find a BN structure which maximises marginal likelihood (BDe score). Integer programming, specifically the SCIP framework, is used to solve this optimisation problem. Acyclicity constraints are added to the integer program (IP) during solving in the form of *cutting planes*. Finding good cutting planes is the key to the success of the approach---the search for such cutting planes is effected using a sub-IP. Results are good with optimal BNs being found substantially faster than competing approaches. I will also discuss whether 'variable pricing' can be used to remove the parent set size limitation.