A Sparse Structure Learning Algorithm for Bayesian Network Identification from Discrete High-Dimensional Data

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 that satisfies the sparsity and the DAG property simultaneously. 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 in 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 the others in evaluation metrics.