{"type":"ScholarlyArticle","title":"Bayesian Network Structure Learning with Integer Programming: Polytopes, Facets and Complexity (Extended Abstract)","authors":[{"name":"James Cussens","slug":"james-cussens","given":"James","family":"Cussens","affiliation":"University of York United Kingdom"},{"name":"Matti Järvisalo","slug":"matti-jarvisalo","given":"Matti","family":"Järvisalo","affiliation":"University of Helsinki Finland"},{"name":"Janne H. Korhonen","slug":"janne-h-korhonen","given":"Janne H.","family":"Korhonen","affiliation":"Aalto University Finland"},{"name":"Mark Bartlett","slug":"mark-bartlett","given":"Mark","family":"Bartlett","affiliation":"University of York United Kingdom"}],"abstract":"Developing accurate algorithms for learning structures of probabilistic graphical models is an important problem within modern AI research. Here we focus on score-based structure learning for Bayesian networks as arguably the most central class of graphical models. A successful generic approach to optimal Bayesian network structure learning (BNSL), based on integer programming (IP), is implemented in the Gobnilp system. Despite the recent algorithmic advances, current understanding of foundational aspects underlying the IP based approach to BNSL is still somewhat lacking. In this paper, we provide theoretical contributions towards understanding fundamental aspects of cutting planes and the related separation problem in this context, ranging from NP-hardness results to analysis of polytopes and the related facets in connection to BNSL.","doi":"10.24963/ijcai.2017/708","url":"https://ijcai.org/proceedings/2017/708","pdf":"https://ijcai.org/proceedings/2017/0708.pdf","markdown":"https://ijcai.org/proceedings/2017/708.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/708","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Journal track","track":"Journal track","number":708,"pages":{"first":4990,"last":4994},"keywords":["Machine Learning: Learning Graphical Models","Uncertainty in AI: Bayesian Networks","Knowledge Representation, Reasoning, and Logic: Computational Complexity of Reasoning","Constraints and Satisfiability: Constraint Optimisation"],"videos":[],"references":[{"position":1,"raw":"[Achterberg, 2007] Tobias Achterberg. 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