# When are epsilon-nets small?

arXiv: https://arxiv.org/abs/1711.10414 · HTML: https://mlsanity.com/paper/1711.10414/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Nov 2017.

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

- [The One-Inclusion Graph Algorithm is not Always Optimal](https://mlsanity.com/paper/2212.09270/) (2022)
- [Is Transductive Learning Equivalent to PAC Learning?](https://mlsanity.com/paper/2405.05190/) (2024)
- [Uniform Mean Estimation for Heavy-Tailed Distributions via Median-of-Means](https://mlsanity.com/paper/2506.14673/) (2025)
- [Low-degree learning and the metric entropy of polynomials](https://mlsanity.com/paper/2203.09659/) (2022)

## Abstract (arXiv)

In many interesting situations the size of epsilon-nets depends only on ε together with different complexity measures. The aim of this paper is to give a systematic treatment of such complexity measures arising in Discrete and Computational Geometry and Statistical Learning, and to bridge the gap between the results appearing in these two fields. As a byproduct, we obtain several new upper bounds on the sizes of epsilon-nets that generalize/improve the best known general guarantees. In particular, our results work with regimes when small epsilon-nets of size o(frac1ε) exist, which are not usually covered by standard upper bounds. Inspired by results in Statistical Learning we also give a short proof of the Haussler's upper bound on packing numbers.