Mutual Information-Guided GA for Bayesian Network Structure Learning

Abstract

Bayesian network structure learning (BNSL) from data is an NP-hard problem. Genetic algorithms are powerful for solving combinatorial optimization problems, but the lack of effective guidance results in slow convergence and low accuracy regarding BNSL. To address this problem, we propose a mutual information (MI) guided genetic algorithm (MIGA) for BNSL in this paper, which uses MI to effectively search BN structures. In the initialization phase of MIGA, the population is generated by adding additional constraints based on MI to reach a higher score without losing diversity. By employing normalized MI and defining the population support, the potential dominance in the population can be identified and then used to design a novel crossover operator in order to preserve the dominant genes with a higher probability. Moreover, with the guidance of MI for removing loops from the structures, infeasible solutions can be handled in a straightforward and practical way. The proposed MIGA is evaluated on eleven well-known benchmark datasets and compared with four GA-based methods and four other state-of-the-art BNSL algorithms. Experimental results show that MIGA outperforms the compared algorithms in convergence and learning accuracy.