# A Note on the Chernoff Bound for Random Variables in the Unit Interval

arXiv: https://arxiv.org/abs/2205.07880 · HTML: https://mlsanity.com/paper/2205.07880/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 2 references that are in the map.
- First posted on arXiv 15 May 2022.

## Built on by (most cited first, 7 of 7)

- [Split-kl and PAC-Bayes-split-kl Inequalities for Ternary Random Variables](https://mlsanity.com/paper/2206.00706/) (2022)
- [Tighter PAC-Bayes Generalisation Bounds by Leveraging Example Difficulty](https://mlsanity.com/paper/2210.11289/) (2022)
- [Recursive PAC-Bayes: A Frequentist Approach to Sequential Prior Updates with No Information Loss](https://mlsanity.com/paper/2405.14681/) (2024)
- [A Note on the Efficient Evaluation of PAC-Bayes Bounds](https://mlsanity.com/paper/2209.05188/) (2022)
- [Bound to Disagree: Generalization Bounds via Certifiable Surrogates](https://mlsanity.com/paper/2602.23128/) (2026)
- [Sample Compression for Self Certified Continual Learning](https://mlsanity.com/paper/2503.10503/) (2025)
- [Deep Actor-Critics with Tight Risk Certificates](https://mlsanity.com/paper/2505.19682/) (2025)

## Abstract (arXiv)

The Chernoff bound is a well-known tool for obtaining a high probability bound on the expectation of a Bernoulli random variable in terms of its sample average. This bound is commonly used in statistical learning theory to upper bound the generalisation risk of a hypothesis in terms of its empirical risk on held-out data, for the case of a binary-valued loss function. However, the extension of this bound to the case of random variables taking values in the unit interval is less well known in the community. In this note we provide a proof of this extension for convenience and future reference.