# Robust Nonparametric Regression under Huber's ε-contamination Model

arXiv: https://arxiv.org/abs/1805.10406 · HTML: https://mlsanity.com/paper/1805.10406/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 May 2018.

## Built on by (most cited first, 6 of 6)

- [Policy Gradient Method For Robust Reinforcement Learning](https://mlsanity.com/paper/2205.07344/) (2022)
- [Robust Constrained Reinforcement Learning](https://mlsanity.com/paper/2209.06866/) (2022)
- [Near-Optimal Policy Identification in Robust Constrained Markov Decision Processes via Epigraph Form](https://mlsanity.com/paper/2408.16286/) (2024)
- [Adversarial Regression with Doubly Non-negative Weighting Matrices](https://mlsanity.com/paper/2109.14875/) (2021)
- [Robust Regression with Ensembles Communicating over Noisy Channels](https://mlsanity.com/paper/2408.10942/) (2024)
- [Provably Outlier-resistant Semi-parametric Regression for Transferable Calibration of Low-cost Air-quality Sensors](https://mlsanity.com/paper/2511.19810/) (2025)

## Abstract (arXiv)

We consider the non-parametric regression problem under Huber's ε-contamination model, in which an ε fraction of observations are subject to arbitrary adversarial noise. We first show that a simple local binning median step can effectively remove the adversary noise and this median estimator is minimax optimal up to absolute constants over the H"older function class with smoothness parameters smaller than or equal to 1. Furthermore, when the underlying function has higher smoothness, we show that using local binning median as pre-preprocessing step to remove the adversarial noise, then we can apply any non-parametric estimator on top of the medians. In particular we show local median binning followed by kernel smoothing and local polynomial regression achieve minimaxity over H"older and Sobolev classes with arbitrary smoothness parameters. Our main proof technique is a decoupled analysis of adversary noise and stochastic noise, which can be potentially applied to other robust estimation problems. We also provide numerical results to verify the effectiveness of our proposed methods.