Euclidean mirrors and first-order changepoints in network time series

Euclidean mirrors and first-order changepoints in network time series
Dr. Zachary Lubberts
Assistant Professor of Statistics
University of Virginia
  
Friday, February 14th, 2025 
11:00 A.M. – 12:00 P.M. Eastern Time 
George Mason University
Nguyen Engineering Building, Jajodia Auditorium, Room 1101 
4511 Patriot Circle, Fairfax, Virginia 22030
The seminar talk is also live-streamed. Please (https://nam11.safelinks.protection.outlook.com/?url=https%3A%2F%2Fforms.office.com%2Fr%2FiKmfG9TRfL&data=05%7C02%7Ckhassan1%40gmu.edu%7Ce68f0039cf52432c66c808dd4ab57147%7C9e857255df574c47a0c00546460380cb%7C0%7C0%7C638748865415063328%7CUnknown%7CTWFpbGZsb3d8eyJFbXB0eU1hcGkiOnRydWUsIlYiOiIwLjAuMDAwMCIsIlAiOiJXaW4zMiIsIkFOIjoiTWFpbCIsIldUIjoyfQ%3D%3D%7C0%7C%7C%7C&sdata=1D2gQLkg7uv19bP2BlNWzEai3uqtgwiCO3DLlEQitbQ%3D&reserved=0) to receive the link.
 
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.
Bio: 
Zach Lubberts is a data scientist working on the interplay of statistics and optimization, with an emphasis on statistics on graphs. Some of his recent publications concern accurate estimation of the eigenvectors of random matrices and the capture of relevant signal in various graph models, including time series of graphs.
Lubberts earned his Ph.D. in applied mathematics and statistics from Johns Hopkins University in 2019. His dissertation research focused on the application of real algebraic geometry to the construction of multivariable tight wavelet frames for use in signal processing. He also earned his bachelor’s degree in applied mathematics and statistics and philosophy from Johns Hopkins in 2013.
Room: Jajodia Auditorium Room 1101, Bldg: Nguyen Engineering Building, , George Mason University, 4511 Patriot Circle, Fairfax, Virginia, United States, 22030, Virtual: https://events.vtools.ieee.org/m/468380