# Bibliography

Research Report

### On polyhedral approximations of polytopes for learning Bayes nets

,

**: **ÚTIA AV ČR,
(Praha 2011)

**: **Research Report 2303

**: ** CEZ:AV0Z10750506

**: **GA201/08/0539, GA ČR

**: **learning Bayesian networks,
imsets,
polytopes

**(eng): **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.

**: **BA