Euclidean mirrors and first-order changepoints in network time series

2024/05/17 by Chen, Tianyi, Lubberts, Zachary, Athreya, Avanti +2 · 2 citations
#FOS: Computer and information sciences #Methodology (stat.ME)

paper · doi:10.48550/arxiv.2405.11111

Abstract

We describe a model for a network time series whose evolution is governed by an underlying stochastic process, known as the latent position process, in which network evolution can be represented in Euclidean space by a curve, called the Euclidean mirror. We define the notion of a first-order changepoint for a time series of networks, and construct a family of latent position process networks with underlying first-order changepoints. We prove that a spectral estimate of the associated Euclidean mirror localizes these changepoints, even when the graph distribution evolves continuously, but at a rate that changes. Simulated and real data examples on organoid networks show that this localization captures empirically significant shifts in network evolution.

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