Research On The Structure Learning Of Bayesian Networks Based On Small Sample Data

Over the past thirty years, with the development of artificial intelligence, Bayesian networks used in uncertainty problems have gradually aroused researchers' attentions. Because of the limitation of objective factors, it has difficulties in gathering enough sample data in the practical applications, so it is very necessary to research on the structure learning of Bayesian networks based on small sample data. In this paper, two different algorithms are proposed to learn the structure of Bayesian networks: the structure learning of Bayesian networks based on small sample and the structure learning of Bayesian networks based on improved AF algorithm.In this paper, a new hybrid algorithm—MM&EOS is presented to recover the structure of Bayesian networks based on small sample data. A PDAG is constructed in three consecutive stages. The first stage learns associations between variables for constructing an undirected structure. A new method of MMCMI(mutual min conditional mutual information) algorithm is introduced to recover an undirected structure. A relaxation fator is introduced in order to reduce the size of the condition set. In the second stage, the EOS algorithm is used to direct edges based on an undirected structure recovered in the first stage. In the third stage, undirected edges are directed by employing orientation rules as far as possible. According to the experimental result, our algorithm has advantages over PC algorithm in term of the structure accuracy. In addition, the accuracy of the undirected graphs obtained in the first stage will have a great influence on orientation process. Hence MMCMI was compared with MMPC and MI in term of the correctness of structure.The IAF algorithm proposed for learning the structure of Bayesian networks is the combination the proporties of score function with AF algorithm. According to the proporties of score function, the highest score network structure is obtained without exhaustive search. But there may exist directed cycles. In this paper, the IAF algorithm is utilized to break each directed cycle randomly and search the optimal Bayesian network structure with guarantance on each iteration on the DAG. Owing to the global optimization search ability, the simulation experiments on Alarm network show that IAF algorithm has advantages over MMHC algorithm in term of the structure accuracy.