0475614 20240103214203.320170623235959.9 85021109619 000407655600014 10.1016/j.ijar.2017.06.001 23 s. P cav_un_epca*02567740888-613X881 (2017)259-281Elsevier 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/2017/MTR/studeny-0475614.pdf cav_un_auth*0332303 GA16-12010S GA ČR CZ 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. cav_un_auth*0347198 8th International Conference of Probabilistic Graphical Models 20160906 20160909 Lugano CH BA 10000 10100 10103 2018 2 RVO:67985556 http://hdl.handle.net/11104/0272346 S 3+4 Article Computer Science Artificial Intelligence 3+4 Article Computer Science Artificial Intelligence 3+4 Article Computer Science Artificial Intelligence COMPUTERSCIENCE.ARTIFICIALINTELLIGENCE 2.504 0.687 7.8 0.0042 0.658 3384 0.866 1.343 182 Q2 44.33 51.1 Q3 Q2 0.9 Q2 51.136 2017 85021109619 SCOPUS PUBMED 000407655600014 WOS cav_un_epca*0256774 International Journal of Approximate Reasoning 0888-613X 1873-4731 Roč. 88 č. 1 2017 259 281 Elsevier