0363159 20240103195438.420110913235959.9 Praha ÚTIA AV ČR 2011 31 s. Research Report 2303 learning Bayesian networks imsets polytopes cav_un_auth*0101202 Studený Milan Matematická teorie rozhodování Department of Decision Making Theory MTR MTR UTIA-B Department of Decision Making Theory Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0274176 Haws D. US http://library.utia.cas.cz/separaty/2011/MTR/studeny-on polyhedral approximations of polytopes for learning bayes nets.pdf GA201/08/0539 GA ČR cav_un_auth*0239648 CEZ:AV0Z10750506 We review three vector encodings of Bayesian network structures. The first one has recently been applied by Jaakkola et al., the other two use special integral vectors, called imsets. The central topic is the comparison of outer polyhedral approximations of the corresponding polytopes. We show how to transform the inequalities suggested by Jaakkola et al. to the framework of imsets. The result of our comparison is the observation that the implicit polyhedral approximation of the standard imset polytope suggested in (Studený Vomlel 2010) gives a closer approximation than the (transformed) explicit polyhedral approximation from (Jaakkola et al. 2010). Finally, we confirm a conjecture from (Studený Vomlel 2010) that the above-mentioned implicit polyhedral approximation of the standard imset polytope is an LP relaxation of the polytope. 2012 BA 2 4 O 4o 20231122134635.1 http://hdl.handle.net/11104/0199217 2011 Soubory v repozitáři: 0363159.pdf 2011 Praha ÚTIA AV ČR