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 i...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.展开更多
基金supported by the National Key R&D Program of China (Grant 2020YFA0714102)the National Natural Science Foundation of China (Grant 12171079).
文摘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.
