An Eigenmodel for Dynamic Multilayer Networks

TL;DR

This paper introduces a new latent space model for dynamic multilayer networks that captures shared evolving structures and layer-specific variations, with scalable inference methods demonstrated on real-world data.

Contribution

The paper develops a novel latent space model for dynamic multilayer networks, including identifiability analysis and a scalable variational inference algorithm.

Findings

Accurately estimates shared and layer-specific structures in simulated networks.

Scalable inference method applied successfully to real-world international relations data.

Model reveals meaningful patterns in disease spread and conflict data.

Abstract

Dynamic multilayer networks frequently represent the structure of multiple co-evolving relations; however, statistical models are not well-developed for this prevalent network type. Here, we propose a new latent space model for dynamic multilayer networks. The key feature of our model is its ability to identify common time-varying structures shared by all layers while also accounting for layer-wise variation and degree heterogeneity. We establish the identifiability of the model's parameters and develop a structured mean-field variational inference approach to estimate the model's posterior, which scales to networks previously intractable to dynamic latent space models. We demonstrate the estimation procedure's accuracy and scalability on simulated networks. We apply the model to two real-world problems: discerning regional conflicts in a data set of international relations and quantifying infectious disease spread throughout a school based on the student's daily contact patterns.