# PAC-Bayes Mini-tutorial: A Continuous Union Bound

arXiv: https://arxiv.org/abs/1405.1580 · HTML: https://mlsanity.com/paper/1405.1580/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 May 2014.

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

- [User-friendly introduction to PAC-Bayes bounds](https://mlsanity.com/paper/2110.11216/) (2021)
- [Information Complexity and Generalization Bounds](https://mlsanity.com/paper/2105.01747/) (2021)
- [Tighter Expected Generalization Error Bounds via Convexity of Information Measures](https://mlsanity.com/paper/2202.12150/) (2022)
- [PAC-Bayes Bounds for Bandit Problems: A Survey and Experimental Comparison](https://mlsanity.com/paper/2211.16110/) (2022)

## Abstract (arXiv)

When I first encountered PAC-Bayesian concentration inequalities they seemed to me to be rather disconnected from good old-fashioned results like Hoeffding's and Bernstein's inequalities. But, at least for one flavour of the PAC-Bayesian bounds, there is actually a very close relation, and the main innovation is a continuous version of the union bound, along with some ingenious applications. Here's the gist of what's going on, presented from a machine learning perspective.