Change Point Localization and Inference in Dynamic Multilayer Networks

2025-06-26

AI Summary

This paper addresses offline change-point localization and statistical inference in dynamic multilayer random dot product graphs (D-MRDPGs), a model wherein nodes share latent positions across layers while layer-specific connectivity mechanisms evolve heterogeneously over time. To overcome the lack of theoretical guarantees and interpretable inference in existing approaches, we first establish consistency and asymptotic normality of change-point estimators. We then propose a two-stage algorithm integrating seeded binary segmentation with low-rank tensor estimation to achieve high-precision change-point localization. Furthermore, we develop a fully data-driven confidence interval calibration procedure enabling principled, interpretable statistical inference. Numerical experiments demonstrate that our method significantly outperforms state-of-the-art baselines in both estimating the number and locations of change points.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• Localize change points in dynamic multilayer networks
• Estimate node latent positions and connectivity patterns
• Develop confidence intervals for change point inference

Innovation

• Two-stage algorithm combining seeded binary segmentation
• Low-rank tensor estimation for change points
• Data-driven confidence intervals construction