Learning Bayesian networks using A* search with ancestral constraints

Abstract

When using a Bayesian network to model a practical problem, weak prior knowledge projected as ancestral constraints is necessary. However, it is difficult to directly utilize these non-decomposable constraints using search strategies based on the decomposable score. In this study, we attempt to solve this problem by conducting an implicate path-space search graph and driving the A* algorithm, which is used to obtain the globally optimal solution satisfying the given constraints. We use a maximum covering principle to provide useful pruning rules based on these constraints in the new framework. Moreover, we improve the simple heuristic and the static k-cycle conflict heuristic to adapt to ancestral constraints. We theoretically prove that the new heuristic functions remain admissible and consistent. Our experiments demonstrate that the proposed framework with the new heuristic functions significantly reduces the space complexity of A* search compared with state-of-the-art frameworks, such as Bayesian network graphs and equivalent class trees, when integrating ancestral constraints.