Towards using the chordal graph polytope in learning decomposable models

Milan Studený; James Cussens

Towards using the chordal graph polytope in learning decomposable models

Computer Science

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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 language	English
Pages (from-to)	259-281
Number of pages	23
Journal	International Journal of Approximate Reasoning
Volume	88
Early online date	8 Jun 2017
Publication status	Published - Sept 2017

Bibliographical note

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Cite this

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