Alden Green, Assistant Professor
Department of Applied Mathematics and Statistics
Johns Hopkins University
The High-Dimensional Asymptotics of Principal Components Regression
Abstract: We study principal components regression (PCR) in an asymptotic high-dimensional setting, where the number of data points is proportional to the dimension. We derive exact limiting formulas for estimation and prediction risk, which depend in a complicated manner on the eigenvalues of the population covariance, the alignment between the population PCs and the true signal, and the number of selected PCs. A key challenge in the high-dimensional setting stems from the fact that the sample covariance is an inconsistent estimate of its population counterpart, so that sample PCs may fail to fully capture potential latent low-dimensional structure in the data. We demonstrate this point through several case studies, including that of a spiked covariance model.
This is based on joint work with Elad Romanov.
Bio: Alden is an Assistant Professor in the Johns Hopkins Department of Applied Mathematics and Statistics, where he works on problems related to high-dimensional regression, dimensionality reduction, graph-based nonparametric estimation and hypothesis testing, and selective inference. Previously, he was a Stein Fellow in the Stanford Department of Statistics.He obtained his PhD in Statistics from Carnegie Mellon University, where his thesis was awarded the Umesh K. Gavaskar Memorial Thesis Award. During his PhD, Alden also participated in COVID-19 forecasting efforts as a core member of the DELPHI group.
DATE: Wednesday, October 22, 2025, 3:30 PM, AUST 434
WebEx link:
https://uconn-cmr.webex.com/uconn-cmr/j.php?MTID=m7d20ff55599be3e78c9e8100d5c5db81
Coffee will be available at 3:00 PM in the Noether Lounge (AUST 326)
For more information, contact: Tracy Burke at tracy.burke@uconn.edu