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Journal Article

On polyhedral approximations of polytopes for learning Bayesian networks

Studený Milan, Haws D.C.

: Journal of Algebraic Statistics vol.4, 1 (2013), p. 59-92

: GA201/08/0539, GA ČR

: Bayesian network structure, integer programming, standard imset, characteristic imset, LP relaxation

: http://library.utia.cas.cz/separaty/2013/MTR/studeny-on polyhedral approximations of polytopes for learning bayesian networks.pdf

(eng): 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.

: BA