  This paper considers a Bayesian view for estimating a sub-network in a Markov
random field. The sub-network corresponds to the Markov blanket of a set of
query variables, where the set of potential neighbours here is big. We
factorize the posterior such that the Markov blanket is conditionally
independent of the network of the potential neighbours. By exploiting this
blockwise decoupling, we derive analytic expressions for posterior
conditionals. Subsequently, we develop an inference scheme which makes use of
the factorization. As a result, estimation of a sub-network is possible without
inferring an entire network. Since the resulting Gibbs sampler scales linearly
with the number of variables, it can handle relatively large neighbourhoods.
The proposed scheme results in faster convergence and superior mixing of the
Markov chain than existing Bayesian network estimation techniques.

Machine Learning;Machine Learning