The Study Of The Properties Of Graph Log-linear Models

In the data analysis,the logarithmic linear model advantage can be used to analyze the correlation between variables.However,the high-dimensional logarithmic linear model has some difficulties in the analysis and research of the data.The theory of probability graph model combines the knowledge of probability theory and graph theory,and expresses the dependency relation between random variables by graph,which provides a powerful representation frame for multivariate statistical modeling.Therefore,we use the graph model to analyze the high-dimensional logarithmic linear model intuitively.Combining the Markov network with the basic theory of logarithmic linear model,a logarithmic linear model is established.All the probability graph models can be simplified by means of independent equivalence,and the joint distribution of the model can be simplified by using the conditions of independence,local independence and global independence of the nodes in the probability graph.On the basis of the above,the independence of the variables under the logarithmic linear model and the statistical properties of the model parameters are studied.According to the large group of graph model decomposition,you can get maximum likelihood estimation.The actual data were analyzed statistically.The logarithmic linear model structure and the independence condition of the five-dimensional random variable are analyzed in detail,and the maximum likelihood estimation formula is calculated.Context-specific independence occurs in a variety of forms in a deterministic dependency.Based on the context-specificity of the layer structure model,the maximum likelihood estimation of the logarithmic linear model is studied.