Structural Learning Of Bayesian Networks For Sparse Data

The graph model is widely used to represent and analyze the causal relationship and the conditional independence between the random variables. The graph model mainly includes directed acyclic graphs, undirected graphs and chain diagrams,where the directed acyclic graphs are also called Bayesian networks, the edges of the graph are directed edges, and they can not constitute a directed ring. Bayesian networks is used to describe the causal relationship between random variables.This paper mainly proposed to to learn the algorithm about Bayesian networks structure. There are three main categories learning algorithm about Bayesian net-works structure : 1, based on the independence test of the constraint algorithm; 2,based on the score search algorithm; 3, the algorithm that combines the indepen-dence test and score search.In2008, Xie and Geng have proposed a recursive decomposition algorithm for Bayesian networks structure learning. This algorithm recursively divides large-scale Bayesian networks structure learning problems into smaller scale. The algorithm is mainly applied to the construction of undirected independentgraph, which will lead to two difficulties: first, when the datas are sparse and variables are more ,the structure of undirected independent graphs are not accurate enough; Second, when the variables are more, the construction of undirected graphs is also more complex.In 2013, Cai et al. proposed the Scalable cAusation Discovery Algorithm(SADA). This algorithm divides the variable set V into three sets (V1,C, V2). As long as C is given, there is no direct connection between v1 and V2, and they are not required to be independent, so it is possible to solve the problem of sparse data.However, Cai's algorithm is likely to appear false in the process of merging. In view of this problem, this paper proposes a relearning checking learning algorithm to solve Sparse Data Bayesian Networks Structure Learning Problem, which combines the advantages of Cai's and Xie's algorithms.In this paper, the algorithm of the Bayesian networks are invoked continuously by calling the measurable causal segmentation algorithm. Then, in each group of causal segmentation, the local structure is studied and then merged to obtain the structure that there is false ; finally find the causal segmentation set and its neighbor set, on which call the relearning check algorithm, to correct the learning to get the correct Bayesian networks skeleton graphs.