Change Point Localization and Inference in Dynamic Multilayer Networks

TL;DR

This paper introduces a new method for detecting and inferring change points in dynamic multilayer networks, providing consistent estimation and confidence intervals with strong theoretical guarantees.

Contribution

It presents the first consistent change point localization and inference method for dynamic multilayer networks using a novel two-stage algorithm with tensor estimation.

Findings

The method accurately estimates change points in simulated data.

It constructs valid confidence intervals for change point locations.

The approach outperforms existing methods in numerical experiments.

Abstract

We study offline change point localization and inference in dynamic multilayer random dot product graphs (D-MRDPGs), where at each time point, a multilayer network is observed with shared node latent positions and time-varying, layer-specific connectivity patterns. We propose a novel two-stage algorithm that combines seeded binary segmentation with low-rank tensor estimation, and establish its consistency in estimating both the number and locations of change points. Furthermore, we derive the limiting distributions of the refined estimators under both vanishing and non-vanishing jump regimes. To the best of our knowledge, this is the first result of its kind in the context of dynamic network data. We also develop a fully data-driven procedure for constructing confidence intervals. Extensive numerical experiments demonstrate the superior performance and practical utility of our methods compared to existing alternatives.