Uniform Convergence of Interpolators: Gaussian Width, Norm Bounds, and Benign Overfitting. (arXiv:2106.09276v2 [stat.ML] UPDATED)

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 …

arxiv ml overfitting uniform