  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.
