Vertex misalignment and changepoint localization in network time series

TL;DR

This paper investigates how vertex misalignment affects changepoint detection in dynamic networks, highlighting the importance of marginal and joint distribution information for robust inference.

Contribution

It compares various localization techniques under different models, revealing when misalignment impacts accuracy and when it can be mitigated.

Findings

Vertex misalignment has minimal effect in some models.

Misalignment can significantly impair localization in others.

Graph matching and optimal transport may not always correct misalignment effects.

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.