Decomposition of Covariate-Dependent Graphical Models with Categorical Data (Communications in Mathematical Research, 2023)
Graphical models are wildly used to describe conditional dependence relationships among interacting random variables. Among statisticalinference problems of a graphical model, one particular interest is utilizing itsinteraction structure to reduce model complexity. As an important approachto utilizing structural information, decomposition allows a statistical inferenceproblem to be divided into some sub-problems with lower complexities. In thispaper, to investigate decomposition of covariate-dependent graphical models,we propose some useful definitions of decomposition of covariate-dependentgraphical models with categorical data in the form of contingency tables. Basedon such a decomposition, a covariate-dependent graphical model can be splitinto some sub-models, and the maximum likelihood estimation of this modelcan be factorized into the maximum likelihood estimations of the sub-models.Moreover, some sufficient and necessary conditions of the proposed definitionsof decomposition are studied.