Two or more Bayesian Networks are Markov equivalent when their
corresponding acyclic digraphs encode the same set of conditional independence
(= CI) restrictions. Therefore, the search space of Bayesian
Networks may be organized in classes of equivalence, where each of
them consists of a particular set of CI restrictions. The collection
of sets of CI restrictions obeys a partial order, the graphical Markov
model inclusion partial order, or inclusion order for short.
This paper discusses in depth the role that inclusion order plays in
learning the structure of Bayesian networks. We prove that under very
special conditions the traditional hill-climber always recovers the right
structure.
Moreover, we extend the recent experimental results presented in
(Kocka and Castelo, 2001). We show how learning algorithms for
Bayesian Networks, that take the inclusion order into account, perform
better than those that do not, and we introduce two new ones in
the context of heuristic search and the MCMC method