Any Part of Bayesian Network Structure Learning

We study an interesting and challenging problem, learning any part of a Bayesian network (BN) structure. In this challenge, it will be computationally inefficient using existing global BN structure learning algorithms to find an entire BN structure to achieve the part of a BN structure in which we are interested. And local BN structure learning algorithms encounter the false edge orientation problem when they are directly used to tackle this challenging problem. In this paper, we first present a new concept of Expand-Backtracking to explain why local BN structure learning methods have the false edge orientation problem, then propose APSL, an efficient and accurate Any Part of BN Structure Learning algorithm. Specifically, APSL divides the V-structures in a Markov blanket (MB) into two types: collider V-structure and non-collider V-structure, then it starts from a node of interest and recursively finds both collider V-structures and non-collider V-structures in the found MBs, until the part of a BN structure in which we are interested are oriented. To improve the efficiency of APSL, we further design the APSL-FS algorithm using Feature Selection, APSL-FS. Using six benchmark BNs, the extensive experiments have validated the efficiency and accuracy of our methods.