Bayesian Markov Blanket Estimation

TL;DR

This paper introduces a Bayesian method for efficiently estimating a sub-network, specifically the Markov blanket, within a large Markov random field, enabling faster and scalable inference.

Contribution

It develops a novel Bayesian inference scheme that decouples the Markov blanket estimation from the entire network, improving scalability and convergence speed.

Findings

Linear scaling Gibbs sampler for large neighborhoods

Faster convergence compared to existing methods

Superior mixing of the Markov chain

Abstract

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.