Bayesian network learning with cutting planes

TL;DR

This paper introduces a novel integer programming approach with cutting planes for efficient exact Bayesian network structure learning from complete discrete data, improving speed and accuracy.

Contribution

It presents a new optimization framework using cutting planes within integer programming to effectively enforce acyclicity constraints in Bayesian network learning.

Findings

The method is faster than existing exact learning algorithms.

It effectively enforces acyclicity constraints during optimization.

Results demonstrate high accuracy in learned Bayesian network structures.

Abstract

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.