On polyhedral approximations of polytopes for learning Bayes nets

0363159 - ÚTIA 2012 CZ eng V - Research Report
Studený, Milan - Haws, D.
On polyhedral approximations of polytopes for learning Bayes nets.
Praha: ÚTIA AV ČR, 2011. 31 s. Research Report, 2303.
R&D Projects: GA ČR GA201/08/0539
Institutional research plan: CEZ:AV0Z10750506
Keywords : learning Bayesian networks * imsets * polytopes
Subject RIV: BA - General Mathematics
http://library.utia.cas.cz/separaty/2011/MTR/studeny-on polyhedral approximations of polytopes for learning bayes nets.pdf

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.
Permanent Link: http://hdl.handle.net/11104/0199217