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AMS Special Seminar Series | Alden Green

February 20 @ 10:00 am - 11:00 am

Location: Clark 110

When: February 20th at 10:00 a.m.

Title: 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.  

Bio: Alden is a Stein Fellow in the Stanford Department of 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 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.

Zoom link: https://wse.zoom.us/j/92755277282?pwd=iULpLaFnWAcWl6tQYUbeyZaN3zwBzn.1

Details

Date:
February 20
Time:
10:00 am - 11:00 am
Event Category:

Venue

Clark 110
3400 North Charles Street
Baltimore, Maryland 21218 + Google Map