Integer Linear Programming for the Bayesian network structure learning problem

Bayesian networks are a commonly used method of representing conditional probability relationships between a set of variables in the form of a directed acyclic graph (DAG). Determination of the DAG which best explains observed data is an NP-hard problem [1]. This problem can be stated as a constrain...

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Bibliographic Details
Published in:Artificial intelligence Vol. 244; pp. 258 - 271
Main Authors: Bartlett, Mark, Cussens, James
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.03.2017
Elsevier Science Ltd
Subjects:
Bayesian analysis
Bayesian networks
Conditional probability
Constrained optimisation
Cutting planes
Economic models
Integer Linear Programming
Integer programming
Linear programming
Machine learning
Separation
Constrained optimisation
Separation
Bayesian networks
Cutting planes
Integer Linear Programming
ISSN:0004-3702, 1872-7921
Online Access:Get full text
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Summary:Bayesian networks are a commonly used method of representing conditional probability relationships between a set of variables in the form of a directed acyclic graph (DAG). Determination of the DAG which best explains observed data is an NP-hard problem [1]. This problem can be stated as a constrained optimisation problem using Integer Linear Programming (ILP). This paper explores how the performance of ILP-based Bayesian network learning can be improved through ILP techniques and in particular through the addition of non-essential, implied constraints. There are exponentially many such constraints that can be added to the problem. This paper explores how these constraints may best be generated and added as needed. The results show that using these constraints in the best discovered configuration can lead to a significant improvement in performance and show significant improvement in speed using a state-of-the-art Bayesian network structure learner.
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ISSN:0004-3702
1872-7921
DOI:10.1016/j.artint.2015.03.003