Joint Gaussian Graphical Model Estimation: A Survey

TL;DR

This survey reviews recent methods for estimating joint Gaussian graphical models, emphasizing shared structures across domains, their benefits for high-dimensional data, and challenges posed by data heterogeneity.

Contribution

It provides a comprehensive overview of statistical inference techniques for joint Gaussian graphical models and discusses model selection and simulation strategies.

Findings

Shared structures improve graph estimation in high-dimensional settings.

Data heterogeneity complicates joint model estimation.

Simulations illustrate model performance under various data processes.

Abstract

Graphs from complex systems often share a partial underlying structure across domains while retaining individual features. Thus, identifying common structures can shed light on the underlying signal, for instance, when applied to scientific discoveries or clinical diagnoses. Furthermore, growing evidence shows that the shared structure across domains boosts the estimation power of graphs, particularly for high-dimensional data. However, building a joint estimator to extract the common structure may be more complicated than it seems, most often due to data heterogeneity across sources. This manuscript surveys recent work on statistical inference of joint Gaussian graphical models, identifying model structures that fit various data generation processes. Simulations under different data generation processes are implemented with detailed discussions on the choice of models.