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Multiple and multilevel graphical models
Author(s) -
Kim Inyoung,
Shan Liang,
Lin Jiali,
Gao Wenyu,
Kim ByungJun,
Mahmoud Hamdy
Publication year - 2020
Publication title -
wiley interdisciplinary reviews: computational statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.693
H-Index - 38
eISSN - 1939-0068
pISSN - 1939-5108
DOI - 10.1002/wics.1497
Subject(s) - graphical model , statistical graphics , computer science , graphics , gaussian , conditional dependence , data mining , random variate , data visualization , dependency (uml) , markov chain , hierarchical database model , statistical model , univariate , theoretical computer science , visualization , multivariate statistics , artificial intelligence , machine learning , random variable , mathematics , statistics , computer graphics (images) , physics , quantum mechanics
Abstract Graphical models have played an important role in inferring dependence structures, discovering multivariate interactions among high‐dimensional data associated with classes of interest such as disease status, and visualizing their association. When data are modeled with Gaussian Markov random fields, the graphical model is called a Gaussian graphical model. It has been used to investigate the conditional dependency structure between random variables by estimating sparse precision matrices. Although the Gaussian model has been widely applied, the normality assumption is rather restrictive. Hence, several methods have been proposed under assumptions weaker than the Gaussian assumptions to handle continuous, discrete, and mixed data. However, modeling data of heterogeneous classes and multilevel networks still poses challenges. Addressing these challenges stresses open problems and points out new directions for research. In this article, we review various undirected graphical models for multiple, joint, and multilevel graphs. This article is categorized under: Statistical Models > Graphical Models Statistical and Graphical Methods of Data Analysis > Statistical Graphics and Visualization