Analyzing multi-layer networks via graphex models
Abstract
Networks are crucial for analyzing interactions among coordinating agents, and are thus critical to the intelligence community. The traditional network formulation is tailored to one-layer networks, which represent a single type of interaction among the vertices. In sharp contrast, it is now well-understood that the same set of agents usually interact across distinct modalities —for example, the vertices could represent adversaries, and they might communicate over several distinct mediums of communication. Existing one-layer networks fail to capture such multi-modal interactions among network agents. Multi-layer networks have naturally been proposed to overcome this limitation. Unfortunately, existing multi-layer network models are quite simplistic, and lack the flexibility and expressive power required to accurately capture the structural complexities of real life multi-layer networks. This project aims to overcome this challenge, and develop a set of novel models for multi-layer networks. Furthermore, the proposed research will develop statistically optimal procedures for latent signal recovery in this setup. Specifically, this proposal will focus on the following broad questions-(i) Graphex models with multi-layer interactions- We will develop a new theoretical framework for multi-layer networks. Under this novel formulation, the connections among the nodes will be governed by an underlying parameter, termed as a multi-layer graphex. Subsequently, we will rigorously characterize the theoretical properties of the resulting models, e.g. sparsity, degree distribution, clusteredness etc. Finally, we will develop approximate sampling algorithms for these models—this will facilitate efficient visualization of the resulting networks. (ii) Parameter estimation in multigraphexes- We will develop statistical estimators for the associated multi-layer graphex parameters, and rigorously establish their optimality. Furthermore, we will develop efficient numerical implementations of these estimators, and deploy them on publicly available datasets. (iii) Community detection in multi-layer graphexes- Community detection in multi-layer networks is of natural interest in several modern applications. Existing theoretical analyses are carried out on stylized models, which fail to capture the characteristics of real data. We will investigate this problem under the multi-layer graphex framework, leveraging the PI’s expertise in this area. Further, in practice, the statistician often observes auxiliary node covariates (e.g. demographic information in social networks) which can be helpful for community detection. The statistical impact of this side-information will be rigorously investigated, building on the PIs past research (26, 46).
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Mar 06, 2024
- Source ID
- FA95502310429
Entities
People
- Subhabrata Sen
Organizations
- Air Force Office of Scientific Research
- President and Fellows of Harvard College
- United States Air Force