Benign overfitting and adaptive nonparametric regression

TL;DR

This paper introduces an estimator in nonparametric regression that interpolates data points with high probability and adapts to unknown smoothness, achieving minimax optimal rates.

Contribution

It presents a novel adaptive interpolating estimator that attains optimal rates without prior knowledge of smoothness in nonparametric regression.

Findings

Estimator interpolates data with high probability

Achieves minimax optimal rates adaptively

Works across various H"older classes

Abstract

In the nonparametric regression setting, we construct an estimator which is a continuous function interpolating the data points with high probability, while attaining minimax optimal rates under mean squared risk on the scale of H\"older classes adaptively to the unknown smoothness.