Bayesian Network Structure Learning Based on Topological Order and Penalty Likelihood

With the aid of continuous optimization, this work proposes a novel Bayesian network structure learning algorithm, named Bayesian network structural learning algorithm based on node topological ordering and the regularized likelihood estimation (NOE-MLE, in abbreviation). The first stage of this algorithm estimates the topological order of nodes through the least square loss and the maximum acyclic subgraph. While for the second stage, the triangular part of the weighted adjacency matrix of a model structure is estimated. By comparing with the existing structural learning methods based on continuous optimization techniques, numerical experiments show that the proposed algorithm can complete the network structure learning in a shorter time while ensuring the accuracy.