Work

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

Year: 2021

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2106.09276

Authors: Koehler, Frederic, Zhou, Lijia, Sutherland, Danica J., Srebro, Nathan

Institutions: Massachusetts Institute of Technology, University of Chicago, University of British Columbia, Toyota Technological Institute at Chicago

Language: English

Topic: Stochastic Gradient Optimization Techniques

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Canadian Institute for Advanced Research, Office of Naval Research

Awards: AF: RI: Medium: Collaborative Research: Understanding and Improving Optimization in Deep and Recurrent Networks, G133274215, G2823328944, G3517332641, G4353487559, HDR TRIPODS: Collaborative Research: Institute for Data, Econometrics, Algorithms and Learning, G6543566890, G8006577219, G8876996369

OpenAlex ID: W3169697178

Cites: 27

Cited by: 9

Related to: 20