BNC-VLA: bayesian network structure learning using a team of variable-action set learning automata

Bayesian Network (BN) is a probabilistic graphical model which describes the joint probability distribution over a set of random variables. One of the most important challenges in the field of BNs is to find an optimal network structure based on an available training dataset. Since the problem of searching the optimal BN structure belongs to the class of NP-hard problems, typically greedy algorithms are used to solve it. In this paper a learning automata-based algorithm has been proposed to solve the BNs structure learning problem. There is a learning automaton corresponding with each random variable and at each stage of the proposed algorithm, named BNC-VLA, a set of learning automata is randomly activated and determined the graph edges that must be appeared in that stage. Finally, the constructed network is evaluated using a scoring function. As BNC-VLA algorithm proceeds, the learning process focuses on the BN structure with higher scores. The convergence of this algorithm is theoretically proved; and also some experiments are designed to evaluate the performance of it. Experimental results show that BNC-VLA is capable of finding the optimal structure of BN in an acceptable execution time; and comparing against other search-based methods, it outperforms them.