IFML Seminar: 04/25/25 - On the Role of Gaussian Covariates in Minimum Norm Interpolation

Abstract: In the literature on benign overfitting in linear models, also referred to as minimum norm interpolation, it is typically assumed that the covariates follow a Gaussian distribution. Existing proofs heavily rely on the Gaussian Minimax Theorem (GMT), making them inapplicable to other distributions in the linear setting. In our work, we are the first to establish matching rates for sub-Gaussian covariates in $\ell_p$-linear regression through a novel approach inspired by modern functional analysis. In this talk, we provide an overview of this proof and explore the role of Gaussian covariates in benign overfitting from a purely geometric perspective.

Bio: Gil is a postdoctoral fellow at ETH Zürich, hosted by Professors Fanny Yang, Andreas Krause, and Afonso Bandeira. Previously, he completed his PhD at MIT under the supervision of Professor Sasha Rakhlin and mentorship of Professor Aditya Guntuboyina (UC Berkeley). His main research interests include statistical learning theory, non-parametric statistics, and high-dimensional statistics. Additionally, he works on empirical process theory, finite-dimensional Banach space theory, and the closely related areas of convex and high-dimensional geometry.