# Benign overfitting and adaptive nonparametric regression

arXiv: https://arxiv.org/abs/2206.13347 · HTML: https://mlsanity.com/paper/2206.13347/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 34 references that are in the map.
- First posted on arXiv 27 Jun 2022.

## Builds on (most cited first, 11 of 11)

- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Benign Overfitting in Linear Regression](https://mlsanity.com/paper/1906.11300/) (2019)
- [Just Interpolate: Kernel "Ridgeless" Regression Can Generalize](https://mlsanity.com/paper/1808.00387/) (2018)
- [To understand deep learning we need to understand kernel learning](https://mlsanity.com/paper/1802.01396/) (2018)
- [Benign overfitting in ridge regression](https://mlsanity.com/paper/2009.14286/) (2020)
- [Fit without fear: remarkable mathematical phenomena of deep learning through the prism of interpolation](https://mlsanity.com/paper/2105.14368/) (2021)
- [Harmless interpolation of noisy data in regression](https://mlsanity.com/paper/1903.09139/) (2019)
- [Overfitting or perfect fitting? Risk bounds for classification and regression rules that interpolate](https://mlsanity.com/paper/1806.05161/) (2018)
- [Does data interpolation contradict statistical optimality?](https://mlsanity.com/paper/1806.09471/) (2018)
- [Consistency of Interpolation with Laplace Kernels is a High-Dimensional Phenomenon](https://mlsanity.com/paper/1812.11167/) (2018)
- [Failures of model-dependent generalization bounds for least-norm interpolation](https://mlsanity.com/paper/2010.08479/) (2020)

## Built on by (most cited first, 3 of 3)

- [A Universal Trade-off Between the Model Size, Test Loss, and Training Loss of Linear Predictors](https://mlsanity.com/paper/2207.11621/) (2022)
- [On damage of interpolation to adversarial robustness in regression](https://mlsanity.com/paper/2601.16070/) (2026)
- [When Kernel Ridge Regression Meets the H"older-Zygmund Class: Minimax Optimality and Failure of Properness](https://mlsanity.com/paper/2607.26065/) (2026)

## Abstract (arXiv)

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.