The Research On Optimal Selection Of Probability Graphical Models Based On Contingency Tables

Considering the optimal matching problem of probability graphical models,a method is proposed in this paper to select the best model of the given data.The process of solving the Markov bases is transformed into algebraic form by searching the generators of the toric ideals with algebraic tools.Then by using the Metropolis-Hastings algorithm,a set of data moving on the periodic,stationary Markov chains are obtained.Taking into account the influence of the ratio of samples under the given distribution to the total samples,calculated by the Metropolis-Hastings algorithm,and the edges,a new criterion based on the weight of dynamic parameters is obtained with W=(1-?)·p+?·edgemax/edgc+1,and the reasonable range of the parameter ? ?(0.0069,0.028)is obtained through the numerical analysis of graphical models.The criterion makes the degree of matching between samples and models more intuitive and all-round,and the flexibility of models' applicability evaluation is improved.