Bayesian Network Structure Learning Using Improved A* with Constraints from Potential Optimal Parent Sets

Abstract

Learning the structure of a Bayesian network and considering the efficiency and accuracy of learning has always been a hot topic for researchers. This paper proposes two constraints to solve the problem that the A* algorithm, an exact learning algorithm, is not efficient enough to search larger networks. On the one hand, the parent–child set constraints reduce the number of potential optimal parent sets. On the other hand, the path constraints are obtained from the potential optimal parent sets to constrain the search process of the A* algorithm. Both constraints are proposed based on the potential optimal parent sets. Experiments show that the time efficiency of the A* algorithm can be significantly improved, and the ability of the A* algorithm to search larger Bayesian networks can be improved by the two constraints. In addition, compared with the globally optimal Bayesian network learning using integer linear programming (GOBNILP) algorithm and the max–min hill-climbing (MMHC) algorithm, which are state of the art, the A* algorithm enhanced by constraints still performs well in most cases.