# Bayesian Markov Blanket Estimation

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Dinu Kaufmann,
Sonali Parbhoo,
Aleksander Wieczorek,
Sebastian Keller,
David Adametz,
Volker Roth
;

Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, PMLR 51:333-341, 2016.

#### Abstract

This paper considers a Bayesian view for estimating 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.

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