Joint Gaussian Graphical Model Estimation: A Survey
It addresses the challenge of data heterogeneity in graph estimation for researchers in statistics and machine learning, but is incremental as a survey.
This survey examines joint Gaussian graphical model estimation, focusing on methods to identify common structures across heterogeneous data sources, and discusses model selection through simulations.
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.