A Multi-Granularity Information-Based Method for Learning High-Dimensional Bayesian Network Structures

The purpose of structure learning is to construct a qualitative relationship of Bayesian networks. Bayesian network with interpretability and logicality is widely applied in a lot of fields. With the extensive development of high-dimensional and low sample size data in some applications, structure learning of Bayesian networks for high dimension and low sample size data becomes a challenging problem. To handle this problem, we propose a method for learning high-dimensional Bayesian network structures based on multi-granularity information. First, an undirected independence graph construction method containing global structure information is designed to optimize the search space of network structure. Then, an improved agglomerative hierarchical clustering method is presented to cluster variables into sub-granules, which reduces the complexity of structure learning by considering the variable community characteristic in high-dimensional data. Finally, the corresponding sub-graphs are formed by learning the internal structure of sub-granules, and the final network structure is constructed based on the proposed construct link graph algorithm. To verify the proposed method, we conduct two types of comparison experiments: comparison experiment and embedded comparison experiment. The results of the experiments show that our approach is superior to the competitors. The results indicate that our method can not only learn structures of Bayesian network from high-dimensional data efficiently but also improve the efficiency and accuracy of network structure generated by other algorithms for high-dimensional data.