Learning And Application Of Bayesian Networks With Hidden Variables

In real world, the phenomenon that we can observe may only represent the partial information of the objective world, and there are many factors which are very important to understand the complex relation, but we cannot observe them directly. Hidden variables can be used to represent the unobservable information, and the appropriate hidden variable not only can reduce data dimension, but also simplify the complicated relationship between variables. Furthermore, it also can eliminate a large number of dependencies and discover the underlying information in the data. The learning of the Bayesian network with hidden variables has become a major topic in the field of artificial intelligence, which is mainly due to the hidden variables can improve the comprehensibility of the models and avoid the over-fitting.Latent tree model (LTM) is a special case of Bayesian network with latent variables, but its structure is more concise than Bayesian network with hidden variables. LTM’s structure is rooted tree where the leaf nodes are observed while the others are hidden. The learning of the LTM is based on the learning of Bayesian networks with hidden variables, and in this article we use the method of search and scoring combined with the Dependency analysis to learn the LTM.Expectation maximization (EM) algorithm is suitable for learning models with latent variables, and it can converge quickly, yet it belongs to local greedy search algorithm and is sensitive to initial values, so it is likely to fall into the local optimal value. In this paper, we use Gibbs sampling to learn the latent tree models instead of EM algorithm, which make the parameter iterations converge to the global stationary distribution, thereby it overcomes the defect of EM.Risk assessment is very important to stable business operation of company, this article will apply the theory of LTM to risk assessment. The latent variables in LTM represent the objects that be observed directly, such as:financial risk, operation risk, etc, then construct the latent tree model with a large number of data. When the model structure is determined, we can start to learn parameters, then the prediction of risk grade is obtained. Therefore the prediction will provide corresponding support to decision-makers.