BIC-based node order learning for improving Bayesian network structure learning

Node order is one of the most important factors in learning the structure of a Bayesian network (BN) for probabilistic reasoning. To improve the BN structure learning, we propose a node order learning algorithm based on the frequently used Bayesian information criterion (BIC) score function. The algorithm dramatically reduces the space of node order and makes the results of BN learning more stable and effective. Specifically, we first find the most dependent node for each individual node, prove analytically that the dependencies are undirected, and then construct undirected subgraphs UG. Secondly, the UG is examined and connected into a single undirected graph UGC. The relation between the subgraph number and the node number is analyzed. Thirdly, we provide the rules of orienting directions for all edges in UGC, which converts it into a directed acyclic graph (DAG). Further, we rank the DAG’s topology order and describe the BIC-based node order learning algorithm. Its complexity analysis shows that the algorithm can be conducted in linear time with respect to the number of samples, and in polynomial time with respect to the number of variables. Finally, experimental results demonstrate significant performance improvement by comparing with other methods