0462009 20240103212527.020160829235959.9 85021109619 10.1016/j.ijar.2017.06.001 12 s. E cav_un_epca*0462433Proceedings of the Eighth International Conference on Probabilistic Graphical Models499-510BrooklineMicrotome Publishing2016AntonucciA.CoraniG.Polpo de CamposC. learning decomposable models integer linear programming characteristic imset chordal graph polytope clutter inequalities separation problem cav_un_auth*0101202 Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory Studený Milan UTIA-B Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0332730 Cussens J. GB http://library.utia.cas.cz/separaty/2016/MTR/studeny-0462009.pdf cav_un_auth*0332303 GA16-12010S GA ČR CZ 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 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. 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. cav_un_auth*0332731 the Eighth International Conference on Probabilistic Graphical Models 06.09.2016-09.09.2016 Lugano CH BA 2017 2 PR RVO:67985556 http://hdl.handle.net/11104/0261903 S 2016 85021109619 SCOPUS cav_un_epca*0462433 Proceedings of the Eighth International Conference on Probabilistic Graphical Models Microtome Publishing 2016 Brookline 499 510 JMLR: Workshop and Conference Proceedings vol. 52 1938-7228 340 Antonucci A. 340 Corani G. 340 Polpo de Campos C.