Research output: Contribution to journal › Article › peer-review

**Towards using the chordal graph polytope in learning decomposable models.** / Studený, Milan; Cussens, James.

Research output: Contribution to journal › Article › peer-review

Studený, M & Cussens, J 2017, 'Towards using the chordal graph polytope in learning decomposable models', *International Journal of Approximate Reasoning*, vol. 88, pp. 259-281.

Studený, M., & Cussens, J. (2017). Towards using the chordal graph polytope in learning decomposable models. *International Journal of Approximate Reasoning*, *88*, 259-281.

Studený M, Cussens J. Towards using the chordal graph polytope in learning decomposable models. International Journal of Approximate Reasoning. 2017 Sep;88:259-281.

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title = "Towards using the chordal graph polytope in learning decomposable models",

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.",

author = "Milan Studen{\'y} and James Cussens",

note = "{\textcopyright}2017 Elsevier Inc. All rights reserved. This is an author-produced version of the published paper. Uploaded in accordance with the publisher{\textquoteright}s self-archiving policy.",

year = "2017",

month = sep,

language = "English",

volume = "88",

pages = "259--281",

journal = "International Journal of Approximate Reasoning",

issn = "0888-613X",

publisher = "Elsevier",

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T1 - Towards using the chordal graph polytope in learning decomposable models

AU - Studený, Milan

AU - Cussens, James

N1 - ©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.

PY - 2017/9

Y1 - 2017/9

N2 - 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.

AB - 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.

M3 - Article

VL - 88

SP - 259

EP - 281

JO - International Journal of Approximate Reasoning

JF - International Journal of Approximate Reasoning

SN - 0888-613X

ER -