Gaussian Graph Model And Independence Research

The probability graphical model uses the nodes and edges of graph to represent the probability distribution,and establishes the connection between the probability theory and the graph theory.Based on continuous variables,gaussian graphical model occupies an important position in dealing with multivariate correlation analysis,and provides a powerful framework for multivariate statistical modeling.This paper studies the model representation of gaussian graphical model and the corresponding independence knowledge,and gets the new properties of the gaussian graphical model,and gives the calculation method of variance of random variables in the mixed gaussian graphical model.The first part introduces the basic definition of gaussian graphical model and several commonly used gaussian graphical models,such as gaussian graphical model,mixed gaussian graphical model,linear gaussian model,gaussian bayesian network and gaussian markov random field.The second part introduces the random gaussian graphical model,takes the random gaussian graphical model with four nodes as an example,the changes of variance,covariance and correlation coefficient between two random variables are discussed after removing one edge or one node randomly in the gaussian graph model.and then extend it to the gaussian graphical model whose number of nodes is greater than four.The corresponding conclusion is got.The third part discusses the independence of the gaussian graphical model,including local independence and d-separation independence.The t-separation independence of gaussian graphical model is studied by introducing trek.Then,the relation between d-separation and t-separation is explained.The variance method of random variable of mixed gaussian graphical model is obtained by trek rule in the fourth part.At the same time,the application of gaussian graphical model in the study of the correlation of variables is introduced.Finally,a summary of the article is made.Meanwhile,the research that the t-separation will be faced in the discrete case of random variables is continuing.