Learning Method Of Hidden Variables Model Based On Structure

With the rapid development of data acquisition/processing mechanisms, cloud computing and Web2.0like novel information services, uncertainty in artificial intelligence and computational intelligence have attracted much interest in data analysis and knowledge discovery. Uncertainty has become an ubiquitous kind of knowledge in various applications. It has been played a key role for researching and solving the problems. Bayesian network (BN) is a directed acyclic graph that each node is annotated with a conditional probability distribution. It is one of the most effective theoretical models for representing and inferring uncertain knowledge. In realistic situations, some variables are objectively existent but can never be observed, called latent variables (LVs). Correspondingly, BN with LVs is generally called latent variable model, where LVs play a central role for real-life problems. LVs can bring together the complex dependencies among observed variables, and make the fully observable structure more concise and the relationships among observed variables more apparent.Latent variable model provides a concise and straightforward framework for representing and inferring uncertain knowledge with unobservable variables or with regard to missing data. In the last decade, two representative classes of algorithms for learning a latent variable model from data include clique-based and cluster-based ones, which simplify the model by a clique and linear or tree structure respectively. By a straightforward comparison, the former class of methods makes the graphical model preserved while the latter class makes the originally arbitrary dependency relationships be neglected.Also in line with the tendency of efficiency improvement in the paradigm of latent variable model research, we propose the information theory based concept of existence weight and incorporate it into the clique-based learning method. In line with the challenges when learning BN with LVs, we focus on determining the number of LVs, and determining the relationships between LVs and the observed variables. First, we define the existence weight and propose the algorithms for finding the ε-cliques from the BN without LVs learned from data. Then, we introduce the LV to each ε-clique and adjust the BN structure with LVs. Further, we adjust the value of parameter ε to determine the number of LVs.In this paper, we will give the proofs that our method can generally combine the classical clique-based learning methods, and make the latent variable model be more consistent with the realistic situations. Therefore, theoretical and experimental results show the feasibility of our method.