Does data interpolation contradict statistical optimality?

TL;DR

This paper demonstrates that data interpolation methods can attain statistically optimal rates in nonparametric regression and prediction tasks, challenging traditional beliefs about overfitting.

Contribution

It provides theoretical evidence that interpolating learning methods can be statistically optimal, contradicting the common notion that interpolation leads to poor generalization.

Findings

Interpolating methods can achieve optimal nonparametric regression rates

Interpolation does not necessarily imply overfitting or poor prediction

Theoretical results challenge traditional views on data fitting

Abstract

We show that learning methods interpolating the training data can achieve optimal rates for the problems of nonparametric regression and prediction with square loss.