Bayesian network learning with cutting planes
This work addresses the challenge of exact Bayesian network learning for researchers in machine learning and statistics, though it appears incremental as it builds on existing integer programming techniques with a novel constraint-handling approach.
The authors tackled the problem of learning Bayesian network structures from discrete data by formulating it as an optimization problem to maximize log marginal likelihood, using integer programming with cutting planes for acyclicity constraints, resulting in a particularly fast method for exact learning.
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 log 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 show that this is a particularly fast method for exact BN learning.