Bayesian Markov Blanket Estimation
This addresses computational bottlenecks in Bayesian network estimation for researchers in statistics and machine learning, though it appears incremental.
The paper tackles the problem of estimating Markov blankets in Markov random fields without inferring the entire network, achieving faster convergence and superior mixing of the Markov chain compared to existing Bayesian methods.
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.