18846

Video URL

https://simons.berkeley.edu/talks/uniform-convergence-interpolators-gaussian-width-norm-bounds-and-…

Uniform Convergence of Interpolators: Gaussian Width, Norm Bounds, and Benign Overfitting

(2021). Uniform Convergence of Interpolators: Gaussian Width, Norm Bounds, and Benign Overfitting. The Simons Institute for the Theory of Computing. https://simons.berkeley.edu/talks/uniform-convergence-interpolators-gaussian-width-norm-bounds-and-benign-overfitting

Uniform Convergence of Interpolators: Gaussian Width, Norm Bounds, and Benign Overfitting. The Simons Institute for the Theory of Computing, Dec. 06, 2021, https://simons.berkeley.edu/talks/uniform-convergence-interpolators-gaussian-width-norm-bounds-and-benign-overfitting 

          @misc{ scivideos_18846,
            doi = {},
            url = {https://simons.berkeley.edu/talks/uniform-convergence-interpolators-gaussian-width-norm-bounds-and-benign-overfitting},
            author = {},
            keywords = {},
            language = {en},
            title = {Uniform Convergence of Interpolators: Gaussian Width, Norm Bounds, and Benign Overfitting},
            publisher = {The Simons Institute for the Theory of Computing},
            year = {2021},
            month = {dec},
            note = {18846 see, \url{https://scivideos.org/index.php/Simons-Institute/18846}}
          }
Frederic Koehler (Simons Institute)
Talk number18846
Source RepositorySimons Institute
Subject

Abstract

We consider interpolation learning in high-dimensional linear regression with Gaussian data, and prove a generic uniform convergence guarantee on the generalization error of interpolators in an arbitrary hypothesis class in terms of the class's Gaussian width. Applying the generic bound to Euclidean norm balls recovers the consistency result of Bartlett et al. (2020) for minimum-norm interpolators, and confirms a prediction of Zhou et al. (2020) for near-minimal-norm interpolators in the special case of Gaussian data. We demonstrate the generality of the bound by applying it to the simplex, obtaining a novel consistency result for minimum l1-norm interpolators (basis pursuit). Our results show how norm-based generalization bounds can explain and be used to analyze benign overfitting, at least in some settings. Joint work with Lijia Zhou, Danica Sutherland, and Nathan Srebro.