Research On The Graphical Models In Intelligence Data Processing

Graphical model is a synergy between probabilistic and graphical theory. As a graphical representation, where the nodes are random variables and where the edges(directed or undirected) specify the conditional independence assumptions between these variables, of knowledge, it has become a powerful tool to represent knowledge and reason under uncertainty in a way akin to human intelligence and has been extensively used in expert system, decision analysis, pattern recognition, machine learning and data mining. It has been a rapidly growing research field and has seen a great deal of activity in recent years. The graphical model consists of structure (graph) and parameters (conditional or marginal probabilistic distribution). The structural part describes the dependent relationship between variables quantitatively and the parameters part gives a qualitative description. There are many research topics for graphical model. Some important ones include Bayesian network (directed acyclic graph), Markov network (undirected graph) and chain graph (hybrid graph with both directed and undirected edges). The primary research topics of this dissertation are Bayesian network and Markov network. A brief introduction to chain graph is also included. Applications of graphical model to intelligent data processing and transformations from data to knowledge and from knowledge to intelligence are stressed. The concrete research topics of the dissertation are as follows:1. Graphical Model Learning with Complete Data and Discrete VariablesSome state-of-art algorithms are introduced and analyzed. Two Bayesian network and Markov network structure learning methods are presented. One uses dependency analysis and causal semantic to direct edges and the other is based on basic dependency relationship between variables. By the two methods, questions exist in the state-of-art structure learning algorithms, such as exponential complexity, local optimum in the score-search methods, high-order conditional probability computation and limitation in edge directing, are settled down. Two precision evaluating methods for Bayesian learning algorithms are also introduced. 2. Graphical Model Learning with Incomplete Data and Discrete VariablesIt is quite common that the data available in the structures learning process is incomplete. The incomplete data makes the learning of graphical model directly from data impossible. Therefore, it is a hard and impendent issue to learn graphical model from incomplete data. A typical method to deal with incomplete data is to utilize EM algorithm or some gradient-based optimization methods together with the score-search method. A new method that utilizes the learned structure and Gibbs sampling is presented. As the Gibbs sampling process can converge to global stationary distribution, local optimum problem comes along with the EM algorithm and other gradient-based optimization method can be avoided. In iteration, the joint probability is decomposed according to the learned graphical model and the sampling efficiency improves. The graphical model is regulated continuously and can get to the global stationary distribution asymptotically. The iteration process continues until the stopping criteria are satisfied. Three missing data mechanisms are studied. 1) missing at random: values for each variable are incomplete, but dimensions of variables and some cases are available. 2) with hidden variables or clustering variable: values for the hidden variables or clustering variable is completely missing, no information is available about these variables. 3) data missing in small data set. Multiple cases are unobservable, but dimensions of variables and some cases are available. Methods and algorithms dealing with those three data missing mechanisms are analyzed. Problems with those methods are pointed out. New methods are proposed, and some necessary theories and experimental analyses are given. It is observed that graphical model learning with continuous variables can be transformed into graphical model learning with...