Statistical and Algorithmic Challenges in High-dimensional Robust Estimation by Yeshwanth Cherapanamjeri

Abstract
Building estimators resilient to outliers has remained a cornerstone of statistical research for the past four decades, starting with the seminal work of (Tukey, 1964). However, despite this longstanding interest, very little is known about the computational and statistical properties of these estimators. This talk will explore some of the challenges in designing estimators for arguably the simplest high-dimensional setting: robust mean estimation. In one dimension, the median is a well-known near-optimal estimator, yet classical generalizations to higher dimensions fall short, both statistically and computationally.

I will then present two recent results addressing these shortcomings. The first is a novel high-dimensional, albeit computationally intractable, median with near-optimal statistical performance. The second is a polynomial-time algorithm for computing a high-dimensional median that matches the statistical performance of prior intractable estimators. This construction is based on a new connection to the radial isotropic transformation, which may be of independent interest.

Biography
Yeshwanth is an Assistant Professor in the College of Computing and Data Science at Nanyang Technological University. From 2023–2025, he was a postdoc at MIT, supervised by Constantinos Daskalakis. Before that, he completed his Ph.D at UC Berkeley (2017–2023), advised by Peter Bartlett. His research lies at the intersection of algorithms, statistics, and machine learning, with a focus on designing efficient algorithms for high-dimensional statistics and machine learning with imperfect data.