Structure learning of Bayesian networks by continuous particle swarm optimization algorithms

In this paper, the problem of learning Bayesian network (BN) structures is studied by virtue of particle swarm optimization (PSO) algorithms. After analysing the optimal flying behaviours of some classic PSO algorithms, we put forward a new PSO-based method of learning BN structures. In this method, we treat the position of a particle as an imaginary likelihood that represents to what extent the associated edges exist, treat the velocity as the corresponding increment or decrement of likelihood that represents how the position changes in the process of flying, and treat the BN structures outputted as appendants of positions. The resulting algorithm and its improved version with expert knowledge integrated are illustrated to be efficient in collecting the randomly searched information from all particles. The numerical study based on two bechmarking BNs shows the superiority of our algorithms in the sense of precision, speed, and accuracy.