On polyhedral approximations of polytopes for learning Bayesian networks

0393223 - ÚTIA 2014 RIV US eng J - Journal Article
Studený, Milan - Haws, D.C.
On polyhedral approximations of polytopes for learning Bayesian networks.
Journal of Algebraic Statistics. Roč. 4, č. 1 (2013), s. 59-92. ISSN 1309-3452
R&D Projects: GA ČR GA201/08/0539
Institutional support: RVO:67985556
Keywords : Bayesian network structure * integer programming * standard imset * characteristic imset * LP relaxation
Subject RIV: BA - General Mathematics
http://library.utia.cas.cz/separaty/2013/MTR/studeny-on polyhedral approximations of polytopes for learning bayesian networks.pdf

We review three vector encodings of BN structures. The first one has been used by Jaakkola et al. (2010) and also by Cussens (2011), the other two use special integral vectors formerly introduced, called imsets (Studený, 2005). The topic is the comparison of outer polyhedral approximations of the corresponding polytopes. We show how to transform the inequalities suggested by Jaakkola et al. into the framework of imsets. As a consequence of our results, we confirm a conjecture from (Studený, Vomlel 2011) that the implicit polyhedral approximation of the standard imset polytope considered there is an LP relaxation of that polytope.
Permanent Link: http://hdl.handle.net/11104/0221988