Structural Learning Of Bayesian Networks By Bootstrap

Bayesian network is a model which can describe the relationships between random variables.It represents the conditional independences among random variables by a directed acyclic graph(DAG)and measure the strength of relationships among random variables by conditional probability.Recently,Bayesian network is applied in many fields,such as causal inference,machine learning,psychology.The most important topic in the research of Bayesian network is structural learning,that is to explore the coditional independence relationships among variables from observational data.In this paper,we proposed a structural learning algorithm by bootstrap.In the first step,we get B bootstrap sample sets;in the second step,we learn B DAGs by a structural learning algorithm,and compute maximum likelihood estimations of the Bayesian networks;in the third step,we search a DAG,such that its maximum likelihood estimation is the nearest to the B maximum likelihood estimation accordioning to penalized Kullback-Leibler distance.It should be noted that in the third step we search a DAG whose edges must be included in one of the B DAGs,therefore we can accelerate the searching speed.In this paper,we show that our new algorithm via bootstrap can improve the performance of structural learning through simulation studies.We compare our new algorithm with PC,GES,GDS,GDSM algorithms,and the simulation result show the bootstrap method performs best.Last,we analyze gene expression data with 39 gene and explore their relationship.