Identifying Common Hubs in Multiple Gaussian Graphical Models

Music City Center 

The Gaussian graphical model (GGM) is a useful machine learning and statistics tool to represent relationships of conditional dependence among variables. In many real-world applications, datasets often contain multiple related sub-populations, whose associated GGMs may have common structure. In such cases, it is useful to recover common hub variables, which refers to variables that are highly connected in the GGMs of all sub-populations. In this paper, we propose the Joint Inverse Components for Hub Detection (JIC-HD) method to recover common hubs across multiple GGMs without the need of estimating any GGM explicitly. To this end, we define a notion of joint minimax eigenvectors for multiple precision matrices corresponding to the GGMs, and show that these vectors can recover common hubs in GGMs. We establish theoretical guarantees of common hub recovery in terms of true positive rate (TPR) for our proposed JIC-HD method. Our numerical studies further confirm the superior performance of the JIC-HD in terms of common hub recovery and computational time when compared to several existing methods.

Gaussian graphical model (GGM