arrow
Volume 39, Issue 3
Decomposition of Covariate-Dependent Graphical Models with Categorical Data

Binghui Liu & Jianhua Guo

Commun. Math. Res., 39 (2023), pp. 414-436.

Published online: 2023-04

Export citation
  • 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.

  • AMS Subject Headings

62-09

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CMR-39-414, author = {Liu , Binghui and Guo , Jianhua}, title = {Decomposition of Covariate-Dependent Graphical Models with Categorical Data}, journal = {Communications in Mathematical Research }, year = {2023}, volume = {39}, number = {3}, pages = {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.

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

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.

Binghui Liu & Jianhua Guo. (2023). Decomposition of Covariate-Dependent Graphical Models with Categorical Data. Communications in Mathematical Research . 39 (3). 414-436. doi:10.4208/cmr.2022-0030
Copy to clipboard
The citation has been copied to your clipboard