Year: 2023
Author: Binghui Liu, Jianhua Guo
Communications in Mathematical Research , Vol. 39 (2023), Iss. 3 : pp. 414–436
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2022-0030
Communications in Mathematical Research , Vol. 39 (2023), Iss. 3 : pp. 414–436
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Collapsibility contingency tables covariate-dependent decomposition graphical models.