## Improving Structure MCMC for Bayesian Networks through Markov Blanket Resampling

*Chengwei Su, Mark E. Borsuk*; 17(118):1−20, 2016.

### Abstract

Algorithms for inferring the structure of Bayesian networks from
data have become an increasingly popular method for uncovering
the direct and indirect influences among variables in complex
systems. A Bayesian approach to structure learning uses
posterior probabilities to quantify the strength with which the
data and prior knowledge jointly support each possible graph
feature. Existing Markov Chain Monte Carlo (MCMC) algorithms for
estimating these posterior probabilities are slow in mixing and
convergence, especially for large networks. We present a novel
Markov blanket resampling (MBR) scheme that intermittently
reconstructs the Markov blanket of nodes, thus allowing the
sampler to more effectively traverse low-probability regions
between local maxima. As we can derive the complementary forward
and backward directions of the MBR proposal distribution, the
Metropolis-Hastings algorithm can be used to account for any
asymmetries in these proposals. Experiments across a range of
network sizes show that the MBR scheme outperforms other state-
of-the-art algorithms, both in terms of learning performance and
convergence rate. In particular, MBR achieves better learning
performance than the other algorithms when the number of
observations is relatively small and faster convergence when the
number of variables in the network is large.

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