# Robust Kernel Density Estimation with Median-of-Means principle

arXiv: https://arxiv.org/abs/2006.16590 · HTML: https://mlsanity.com/paper/2006.16590/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jun 2020.

## Built on by (most cited first, 9 of 9)

- [Designing Robust Transformers using Robust Kernel Density Estimation](https://mlsanity.com/paper/2210.05794/) (2022)
- [Adaptive Robust Estimator for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2603.21574/) (2026)
- [Beyond the Known: Adversarial Autoencoders in Novelty Detection](https://mlsanity.com/paper/2404.04456/) (2024)
- [Adversarial Robustness of Nonparametric Regression](https://mlsanity.com/paper/2505.17356/) (2025)
- [Sharp Inequalities between Total Variation and Hellinger Distances for Gaussian Mixtures](https://mlsanity.com/paper/2602.03202/) (2026)
- [Unsupervised Complex Semi-Binary Matrix Factorization for Activation Sequence Recovery of Quasi-Stationary Sources](https://mlsanity.com/paper/2310.02295/) (2023)
- [On the Optimality of the Median-of-Means Estimator under Adversarial Contamination](https://mlsanity.com/paper/2510.07867/) (2025)
- [Wasserstein Filtering: A Sample Selection Method for Robust Distribution Learning](https://mlsanity.com/paper/2608.13418/) (2026)
- [Dual-Channel Robust Group-Relative Policy Optimization via Advantage and Sequence-Weight Estimation](https://mlsanity.com/paper/2609.36944/) (2026)

## Abstract (arXiv)

In this paper, we introduce a robust nonparametric density estimator combining the popular Kernel Density Estimation method and the Median-of-Means principle (MoM-KDE). This estimator is shown to achieve robustness to any kind of anomalous data, even in the case of adversarial contamination. In particular, while previous works only prove consistency results under known contamination model, this work provides finite-sample high-probability error-bounds without a priori knowledge on the outliers. Finally, when compared with other robust kernel estimators, we show that MoM-KDE achieves competitive results while having significant lower computational complexity.