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This paper addresses the problem of learning a sparse structure Bayesiannetwork from high-dimensional discrete data. Compared to continuous Bayesiannetworks, learning a discrete Bayesian network is a challenging problem due tothe large parameter space. Although many approaches have been developed forlearning continuous Bayesian networks, few approaches have been proposed forthe discrete ones. In this paper, we address learning Bayesian networks as anoptimization problem and propose a score function which guarantees the learntstructure to be a sparse directed acyclic graph. Besides, we implement ablock-wised stochastic coordinate descent algorithm to optimize the scorefunction. Specifically, we use a variance reducing method in our optimizationalgorithm to make the algorithm work efficiently for high-dimensional data. Theproposed approach is applied to synthetic data from well-known benchmarknetworks. The quality, scalability, and robustness of the constructed networkare measured. Compared to some competitive approaches, the results reveal thatour algorithm outperforms some of the well-known proposed methods.

A Stochastic Variance-Reduced Coordinate Descent Algorithm for Learning Sparse Bayesian Network from Discrete High-Dimensional Data