Learning cross-layer dependence structure in multilayer networks

TL;DR

This paper introduces a new class of multilayer network models that explicitly capture cross-layer dependencies, extending single-layer models and providing theoretical guarantees and practical methods for analysis.

Contribution

It proposes a separable multilayer network model with theoretical error bounds, model selection, and demonstrates effectiveness through simulations and real data.

Findings

The model accurately captures cross-layer dependencies.

Theoretical error bounds are established for estimators.

Simulation and real data show practical effectiveness.

Abstract

We propose a novel class of separable multilayer network models to capture cross-layer dependencies in multilayer networks, enabling the analysis of how interactions in one or more layers may influence interactions in other layers. Our approach separates the network formation process from the layer formation process, and is able to extend existing single-layer network models to multilayer network models that accommodate cross-layer dependence. We establish non-asymptotic and minimax-optimal error bounds for maximum likelihood estimators and demonstrate the convergence rate in scenarios of increasing parameter dimension. Additionally, we establish non-asymptotic error bounds for multivariate normal approximations and propose a model selection method that controls the false discovery rate. Simulation studies and an application to the Lazega lawyers network show that our framework and method perform well in realistic settings.