Towards using the chordal graph polytope in learning decomposable models

Research output: Contribution to journalArticle (Academic Journal)

Abstract

The motivation for this paper is the integer linear programming approach to learning the structure of a decomposable graphical model. We have chosen to represent decomposable models by means of special zero–one 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. In this theoretical paper, we introduce a class of clutter inequalities (valid for the vectors in the polytope) and show that all of them are facet-defining for the polytope. We dare to conjecture that they lead to a complete polyhedral description of the polytope. Finally, we propose a linear programming method to solve the separation problem with these inequalities for the use in a cutting plane approach.
Original languageEnglish
Pages (from-to)259-281
Number of pages23
JournalInternational Journal of Approximate Reasoning
Volume88
Publication statusPublished - Sep 2017

Bibliographical note

©2017 Elsevier Inc. All rights reserved. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy.

Fingerprint Dive into the research topics of 'Towards using the chordal graph polytope in learning decomposable models'. Together they form a unique fingerprint.

  • Cite this