Research On The Nature Of Chain Graph And Its Inference

Probabilistic graph model combines probability theory with graph theory and provides a framework for multivariable probabilistic statistical model.In the fields of artificial intelligence,machine learning and computer vision,we all use probability graph model.Among them,the chain graph model belongs to the category of probability graph model,which is a probability graph model with both directed and undirected edges,but without directed circles,and provides a powerful model for the causal relationship and correlation between variables.The chain graph is a probabilistic graphical model with both directed edge and undirected edge,but without directed cycles.It provides a powerful framework for complex relationships between variables.In the chain graph model,we base on the variable elimination algorithm of marginal distribution in the Bayesian network,depend on the independence of the chain graph model,use the method of factorization,extend the algorithm to the chain graph model,obtain a variable elimination algorithm based on the marginal probability of the chain graph model.In the calculation process of variable elimination algorithm,we accord to the concept of moral graph of chain graph model,calculate the weight of each node and obtain the variable elimination order,obtain the maximum cardinality search algorithm.On the basis of the maximum cardinality search algorithm,we add a constraint condition,obtain another algorithm for finding the order of eliminating variables--the maximum cardinality search algorithm for computing minimal triangulation.We base on the structure of chain graph model,and give a high-dimensional time series problems,obtain a dynamic chain graph model.We accord to the pair independence and local independence of the chain graph model,extend the independence of the chain graph model,obtain the independence of the dynamic chain graph model.Under the markov hypothesis,we base to the probability distribution of the dynamic model,depend on a variable elimination algorithm in the chain graph model,propose a variable elimination algorithm in the dynamic chain graph model.