TY - JOUR
T1 - Decomposition of Covariate-Dependent Graphical Models with Categorical Data
AU - Liu , Binghui
AU - Guo , Jianhua
JO - Communications in Mathematical Research 
VL - 3
SP - 414
EP - 436
PY - 2023
DA - 2023/04
SN - 39
DO - http://doi.org/10.4208/cmr.2022-0030
UR - https://global-sci.org/intro/article_detail/cmr/21609.html
KW - Collapsibility, contingency tables, covariate-dependent, decomposition, graphical models.
AB - <p style="text-align: justify;">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.</p>