Structural decomposition-based learning of large bayesian networks for detecting conditionally independent overlapping superstructure communities

Community detection is an advanced technique that is employed to facilitate the structural decomposition of large Bayesian networks and enable their learning processes. According to the nonoverlapping community characteristics of Bayesian networks, these networks are broken down into several nonoverlapping smaller subgraphs for learning. However, the learning results of this method are still poor because Bayesian networks are composed of overlapping subgraphs that share causal nodes. A unique decomposition method is introduced in this paper for learning large Bayesian network structures; this approach relies on the principles of overlapping community detection and superstructures. First, to preserve more true dependence relationships so that adjacent nodes are not separated, we present an algorithm for constructing a superstructure, which is an undirected independent graph. Second, to prevent the common parent nodes from being separated, we present a conditionally independent overlapping community detection algorithm to break the superstructure into some overlapping subgraphs. Finally, the subgraphs are individually learned and eventually combined into a whole network. To validate the effectiveness of our method, we conduct a comparative analysis against other famous methods using benchmark networks and large real-world datasets with thousands of variables. The experimental results demonstrate that our method outperforms the state-of-the-art methods.