  Markov networks are extensively used to model complex sequential, spatial,
and relational interactions in a wide range of fields. By learning the
structure of independences of a domain, more accurate joint probability
distributions can be obtained for inference tasks or, more directly, for
interpreting the most significant relations among the variables. Recently,
several researchers have investigated techniques for automatically learning the
structure from data by obtaining the probabilistic maximum-a-posteriori
structure given the available data. However, all the approximations proposed
decompose the posterior of the whole structure into local sub-problems, by
assuming that the posteriors of the Markov blankets of all the variables are
mutually independent. In this work, we propose a scoring function for relaxing
such assumption. The Blankets Joint Posterior score computes the joint
posterior of structures as a joint distribution of the collection of its Markov
blankets. Essentially, the whole posterior is obtained by computing the
posterior of the blanket of each variable as a conditional distribution that
takes into account information from other blankets in the network. We show in
our experimental results that the proposed approximation can improve the sample
complexity of state-of-the-art scores when learning complex networks, where the
independence assumption between blanket variables is clearly incorrect.
