Globally Optimal Structure Learning of Bayesian Networks from Data

The problem of finding a Bayesian network structure which maximizes a score function is known as Bayesian network structure learning from data. We study this problem in this paper with respect to a decomposable score function. Solving this problem is known to be NP-hard. Several algorithms are proposed to overcome this problem such as hill-climbing, dynamic programming, branch and bound, and so on. We propose a new branch and bound algorithm that tries to find the globally optimal network structure with respect to the score function. It is an any-time algorithm, i.e., if stopped, it gives the best solution found. Some pruning strategies are applied to the proposed algorithm and drastically reduce the search space. The performance of the proposed algorithm is compared with the latest algorithm which showed better performance to the others, within several data sets. We showed that the new algorithm outperforms the previously best one.