Multi-Agent Genetic Algorithm for Bayesian networks structural learning

Bayesian networks (BNs) area powerful probabilistic graphical tool for modeling relationships between random variables in an interpretable way. The relationships among variables are represented by the BN structure, a directed acyclic graph, which can be learned from a data set. However, the structural learning process is NP-hard. One popular strategy for learning a BN's structure is the Search and Score approach, where a quality score is defined as the objective function to be optimized. This approach has led to various algorithms, ranging from linear integer programming to heuristics and metaheuristics. In this paper, we present a novel algorithm for BN structure learning, an adaptation of the Multi-Agent Genetic Algorithm designed to tackle the structural learning problem efficiently. Our algorithm was compared to three others across benchmark problems of varying variable sizes, using a randomized factorial design with different sample sizes. Results show our method outperformed others, especially in detecting edge presence and direction, and proved effective for both small and large-scale BN learning, as confirmed by statistical tests.