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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.
}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2022-0030}, url = {http://global-sci.org/intro/article_detail/cmr/21609.html} }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.