Sep 27, 2024
Dear Members of the Editorial Board,
Please find attached our submission, “Euclidean mirrors and first-order changepoints in network time series,” which we hope will be of interest to the editorial board and referees at SIAM Journal on Mathematics of Data Science.
Our manuscript presents a rigorous approach to changepoint localization in networks. 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. To the best of our knowledge, this work is the first theoretical investigation of changepoints of different orders in network time series.
This work has not been published and is not under review elsewhere, and all authors are aware of this submission to SIAM Journal on Mathematics of Data Science and consent to its review.
Thank you for your time and consideration of our manuscript.
Sincerely,
Tianyi Chen, Zachary Lubberts, Avanti Athreya, Youngser Park, and Carey E. Priebe
Johns Hopkins University, Baltimore, MD 21218 and the University of Virginia, Charlottesville, VA 22904