Decomposition of Covariate-Dependent Graphical Models with Categorical Data  

作　　者：Binghui Liu Jianhua Guo 

机构地区：[1]School of Mathematics and Statistics&KLAS,Northeast Normal University,Changchun,Jilin 130024,P.R.China

出　　处：《Communications in Mathematical Research》2023年第3期414-436,共23页数学研究通讯（英文版）

基　　金：supported by the National Key R&D Program of China (Grant 2020YFA0714102);the National Natural Science Foundation of China (Grant 12171079).

摘　　要：Graphical models are wildly used to describe conditional dependence relationships among interacting random variables.Among statistical inference problems of a graphical model,one particular interest is utilizing its interaction structure to reduce model complexity.As an important approach to utilizing structural information,decomposition allows a statistical inference problem to be divided into some sub-problems with lower complexities.In this paper,to investigate decomposition of covariate-dependent graphical models,we propose some useful definitions of decomposition of covariate-dependent graphical models with categorical data in the form of contingency tables.Based on such a decomposition,a covariate-dependent graphical model can be split into some sub-models,and the maximum likelihood estimation of this model can be factorized into the maximum likelihood estimations of the sub-models.Moreover,some sufficient and necessary conditions of the proposed definitions of decomposition are studied.

关 键 词：COLLAPSIBILITY contingency tables covariate-dependent DECOMPOSITION graphical models 

分 类 号：O151.21[理学—数学]