Multiple and multilevel graphical models

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

Gaussian graphical models with applications to omics analyses

“…An example of multi-level data in an omics context is genes and pathways; each gene belongs to one or more pathways, and one can estimate a two-level graphical model consisting of within-pathway edges between genes and between-pathway edges between pathways. 117,118 We close by noting that while GGMs are not a particularly new concept, their utility has been re-emphasized as technology has evolved over the last several decades. In the early 21st century, advances in omics and other big data outpaced existing statistical methods; the development of regularization-based approaches such as the graphical lasso was a transformative step forward.…”

“…A third interesting setting is the case of multi‐level data, where one wishes to construct a graphical model of variables that exist in a hierarchy. An example of multi‐level data in an omics context is genes and pathways; each gene belongs to one or more pathways, and one can estimate a two‐level graphical model consisting of within‐pathway edges between genes and between‐pathway edges between pathways 117,118 …”