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