| Summary: | Learning the structure of Bayesian networks (BNs) from high dimensional discrete data is common nowadays but a challenging task, due to the large parameter space, the acyclicity constraint placed on the graphical structures and the difficulty in searching for a sparse structure. In this article, we propose a sparse structure learning algorithm (SSLA) to solve this problem. The algorithm uses the negative log-likelihood function of multi-logit regression as a loss function, adding the adaptive group lasso as a penalty term for sparsity, with a new penalty term to ensure that the learned graph is a directed acyclic graph. A block coordinate descent algorithm (BCD) combining with the alternating direction multiplier method (ADMM) algorithm is developed to solve the proposed model. The learned graph is proved theoretically to be a Bayesian network. In order to evaluate the proposed SSLA and compare with its competitors, we conducted intensive simulation studies and applied them to the benchmark Bayesian networks. The results indicate that the SSLA is superior to the hill climbing (HC) algorithm, the CD algorithm and the BFO-B algorithm respectively, and is competitive with K2 algorithm when the order of the nodes is given.
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