Vertex misalignment and changepoint localization in network time series

2026-04-21

AI Summary

Node misalignment significantly impairs the accuracy of change point localization in dynamic networks. This study systematically evaluates the performance of several methods—including mean degree statistics, Euclidean embedding with reflection, graph matching, and optimal transport—in detecting change points and correcting alignment errors, using two model classes that share similar change points but differ in their information distribution structures. The findings reveal the critical roles of marginal and joint distributional information in change point localization: misalignment induces negligible effects in one model class but leads to irreversible errors in the other, thereby exposing the limitations of current alignment strategies such as graph matching and optimal transport. The results underscore that robust change point inference necessitates the synergistic integration of both marginal and joint structural information.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Inference for time series of networks often relies on accurate vertex correspondence between network realizations at different times. In practice, however, such vertex alignments can be misspecified or unknown. We study the impact of vertex alignment on changepoint localization for dynamic networks through two illustrative models, each with a similar changepoint, with the key distinction being whether changepoint information is contained in marginal or joint distributions of the time-varying latent positions. We compare localization techniques ranging from the simple network statistic of average degree to the modern procedure of Euclidean mirrors. In one model, vertex misalignment causes little error, and in the other, it impairs localization in ways that cannot be corrected through graph matching or optimal transport, which we show are closely related in this setting. Our results demonstrate that robust network inference necessitates reckoning with the subtle interplay of marginal and joint information in the observed network time series.

Problem

• vertex misalignment
• changepoint localization
• network time series
• dynamic networks
• vertex correspondence

Innovation

• vertex misalignment
• changepoint localization
• dynamic networks
• latent positions
• optimal transport