Algorithmically Testing Sub-Gaussianity of High Dimensional Distributions

Speaker: Ankit Pensia, CMU

General

07 April 2026
606 Seminar Hall, NAC 2
2:30 PM - 3:30 PM

Abstract

Sub-Gaussian distributions play a central role in statistics, probability, and computer science. A distribution is termed sub-Gaussian if all of its univariate projections have tails that decay faster than a Gaussian. In algorithmic statistics, a central task is the following: given samples from a distribution, decide whether the underlying distribution is sub-Gaussian or heavy-tailed. In high dimensions, this is a challenging problem because sub-Gaussianity requires all univariate projections to be light-tailed, which seemingly necessitates a brute-force search over directions to verify. In this talk, I will describe a structural property of sub-Gaussian distributions that leads to computationally efficient algorithms for a wide range of statistical problems, e.g., clustering, robust estimation, and more. Based on joint work with Ilias Diakonikolas, Sam Hopkins, and Stefan Tiegel.

About the Speaker

Ankit Pensia is an assistant professor in the Department of Statistics and Data Science at Carnegie Mellon University. Previously, he was a research fellow at the Simons Institute for the Theory of Computing and a Herman Goldstine Postdoctoral Fellow at IBM Research. He obtained his PhD in Computer Science from the University of Wisconsin-Madison. His current research interests include algorithmic robust statistics, high-dimensional probability, distribution testing, and algorithmic stability.