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

Abstract
The motivation for this paper is the integer linear programming (ILP) 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.

AMS classification 52B12 68T30 90C27

Keywords
integer linear programming
learning decomposable models
characteristic imset
chordal graph polytope
clutter inequalities
separation problem

The contribution builds on the following papers:

Moreover, the paper is an extended version of the conference proceedings paper:

A pdf version (315kB) of a preprint is available.