Identifying Common Hubs in Multiple Gaussian Graphical Models

The Gaussian graphical model (GGM) is a useful 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, as well as large structural differences. In such cases, it is useful to recover common hub variables, which are the highly connected variables in the GGMs of all sub-populations. In this paper, we propose the Joint Inverse Components for Hub Detection (JIC-HD) method to recover the common hubs across multiple GGMs without the need to estimate all subpopulation GGMs. To this end, we introduce joint minimax eigenspaces, and show that these can be leveraged for the recovery of common hubs. We establish theoretical guarantees for the recovery of common hubs. Additionally, our numerical simulation studies confirm superior performance of our JIC-HD in detecting common hubs compared to the existing methods in the literature. Our method is especially advantageous when the multiple GGMs have both common and individual hubs across sub-populations. Finally, we analyze cancer gene-expression datasets and identify biologically meaningful common hub genes across cancer subtypes.

To represent relationships among complex variables (such as genes, economic indexes, or regions of the brain), scientists often use networks where variables are represented as "nodes" and their relationships as connecting links. Within these networks, it is crucial to detect "hub nodes," which refer to nodes that are central and highly connected. For instance, when analyzing gene expression in breast cancer patients, a hub gene might be pivotal in driving the disease, making it a prime target for new therapeutic techniques. However, diseases like cancer often have multiple subtypes, each governed by its own distinct network of genetic relationships, which complicates the analysis. In this work, we develop a novel method designed to detect hubs that are highly connected simultaneously across multiple different networks. When applied to multi-subtype cancer data, our method successfully identifies the key genes relevant to all subtypes, revealing the shared genetic patterns that drive the disease as a whole.