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Algorithmically Testing Sub-Gaussianity of High Dimensional Distributions

Series: Department Seminar

Speaker: Ankit Pensia, Assistant Professor, Department of Statistics and Data Science, Carnegie Mellon University

Date/Time: Feb 26 16:00:00

Location: CSA Auditorium, (Room No. 104, Ground Floor)

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.

Speaker Bio:
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.

Host Faculty: Prof. Anant Raj