A parallel framework for constraint-based bayesian network learning via markov blanket discovery

Bayesian networks (BNs) are a widely used graphical model in machine learning. As learning the structure of BNs is NP-hard, high-performance computing methods are necessary for constructing large-scale networks. In this paper, we present a parallel framework to scale BN structure learning algorithms to tens of thousands of variables. Our framework is applicable to learning algorithms that rely on the discovery of Markov blankets (MBs) as an intermediate step. We demonstrate the applicability of our framework by parallelizing three different algorithms: Grow-Shrink (GS), Incremental Association MB (IAMB), and Interleaved IAMB (Inter-IAMB). Our implementations are able to construct BNs from real data sets with tens of thousands of variables and thousands of observations in less than a minute on 1024 cores, with a speedup of up to 845X and 82.5% efficiency. Furthermore, we demonstrate using simulated data sets that our proposed parallel framework can scale to BNs of even higher dimensionality.