# Optimal Approximations Made Easy

arXiv: https://arxiv.org/abs/2008.08970 · HTML: https://mlsanity.com/paper/2008.08970/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Aug 2020.

## Built on by (most cited first, 2 of 2)

- [Dimension-Independent Kernel ε-Covers](https://mlsanity.com/paper/2306.16516/) (2023)
- [Efficient and Stable Multi-Dimensional Kolmogorov-Smirnov Distance](https://mlsanity.com/paper/2504.11299/) (2025)

## Abstract (arXiv)

The fundamental result of Li, Long, and Srinivasan on approximations of set systems has become a key tool across several communities such as learning theory, algorithms, computational geometry, combinatorics and data analysis. The goal of this paper is to give a modular, self-contained, intuitive proof of this result for finite set systems. The only ingredient we assume is the standard Chernoff's concentration bound. This makes the proof accessible to a wider audience, readers not familiar with techniques from statistical learning theory, and makes it possible to be covered in a single self-contained lecture in a geometry, algorithms or combinatorics course.