# Robust subgaussian estimation with VC-dimension

arXiv: https://arxiv.org/abs/2004.11734 · HTML: https://mlsanity.com/paper/2004.11734/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Apr 2020.

## Built on by (most cited first, 4 of 4)

- [Outlier-Robust Sparse Mean Estimation for Heavy-Tailed Distributions](https://mlsanity.com/paper/2211.16333/) (2022)
- [Computationally Efficient and Statistically Optimal Robust High-Dimensional Linear Regression](https://mlsanity.com/paper/2305.06199/) (2023)
- [Sparse Mean Estimation in Adversarial Settings via Incremental Learning](https://mlsanity.com/paper/2305.15276/) (2023)
- [A Rigorous, Tractable Measure of Model Complexity](https://mlsanity.com/paper/2605.21167/) (2026)

## Abstract (arXiv)

Median-of-means (MOM) based procedures provide non-asymptotic and strong deviation bounds even when data are heavy-tailed and/or corrupted. This work proposes a new general way to bound the excess risk for MOM estimators. The core technique is the use of VC-dimension (instead of Rademacher complexity) to measure the statistical complexity. In particular, this allows to give the first robust estimators for sparse estimation which achieves the so-called subgaussian rate only assuming a finite second moment for the uncorrupted data. By comparison, previous works using Rademacher complexities required a number of finite moments that grows logarithmically with the dimension. With this technique, we derive new robust sugaussian bounds for mean estimation in any norm. We also derive a new robust estimator for covariance estimation that is the first to achieve subgaussian bounds without L4-L2 norm equivalence.