A1407
Title: Euclidean mirrors and first-order changepoints in network time series
Authors: Tianyi Chen - Johns Hopkins University (United States)
Zachary Lubberts - University of Virginia (United States)
Avanti Athreya - Johns Hopkins University (United States) [presenting]
Youngser Park - Johns Hopkins University (United States)
Carey Priebe - Johns Hopkins University (United States)
Abstract: The purpose is to 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. The notion of a first-order changepoint is defined for a time series of networks, and a family of latent position process networks is constructed with first-order changepoints. It is proven 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 brain organoid networks show that this localization captures empirically significant shifts in network evolution.
