How matroids occur in the context of learning Bayesian network structure

0447685 20240103210642.320150925235959.9 84943570009 000493121100085 How matroids occur in the context of learning Bayesian network structure 10 s. P cav_un_epca*0447684978-0-9966431-0-8Uncertainty in Artificial Intelligence, Proceedings of the Thirty-First Conference (2015)832-841Corvallis, OregonAUAI Press2015 learning Bayesian network structure matroid family-variable polytope cav_un_auth*0101202 Department of Decision Making Theory Studený Milan UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2015/MTR/studeny-0447685.pdf cav_un_auth*0292670 GA13-20012S GA ČR It is shown that any connected matroid having a non-trivial cluster of BN variables as its ground set induces a facet-defining inequality for the polytope(s) used in the ILP approach to globally optimal BN structure learning. The result applies to well-known k-cluster inequalities, which play a crucial role in the ILP approach. cav_un_auth*0319865 31st Conference on Uncertainty in Artificial Intelligence 12.07.2015-16.07.2015 Amsterdam NL BA 2016 1 PR RVO:67985556 http://hdl.handle.net/11104/0249568 S 2015 84943570009 SCOPUS 000493121100085 WOS cav_un_epca*0447684 Uncertainty in Artificial Intelligence, Proceedings of the Thirty-First Conference (2015) 978-0-9966431-0-8 832 841 Corvallis, Oregon AUAI Press 2015