Studeny´, Milan and Cussens, James orcid.org/0000-0002-1363-2336 (2016) The Chordal Graph Polytope for Learning Decomposable Models. In: Antonucci, Alessandro, Corani, Giorgio and Polpo de Campos, Cassio, (eds.) Proceedings of the Eighth International Conference on Probabilistic Graphical Models. Journal of Machine Learning Research: Workshop and Conference Proceedings . , pp. 499-510.
Abstract
This theoretical paper is inspired by an integer linear programming (ILP) approach to learning the structure of decomposable models. We intend to represent decomposable models by special zeroone vectors, named characteristic imsets. Our approach leads to the study of a special polytope, defined as the convex hull of all characteristic imsets for chordal graphs, named the chordal graph polytope. We introduce a class of clutter inequalities and show that all of them are valid for (the vectors in) the polytope. In fact, these inequalities are even facet-defining for the polytope and we dare to conjecture that they lead to a complete polyhedral description of the polytope. Finally, we propose an LP method to solve the separation problem with these inequalities for use in a cutting plane approach.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016, The Authors. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details |
Dates: |
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Institution: | The University of York |
Academic Units: | The University of York > Faculty of Sciences (York) > Computer Science (York) |
Depositing User: | Pure (York) |
Date Deposited: | 17 Aug 2016 09:03 |
Last Modified: | 16 Oct 2024 10:48 |
Status: | Published |
Series Name: | Journal of Machine Learning Research: Workshop and Conference Proceedings |
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Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:103832 |