# A Note on the Efficient Evaluation of PAC-Bayes Bounds

arXiv: https://arxiv.org/abs/2209.05188 · HTML: https://mlsanity.com/paper/2209.05188/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 8 references that are in the map.
- First posted on arXiv 12 Sep 2022.

## Builds on (most cited first, 5 of 5)

- [Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data](https://mlsanity.com/paper/1703.11008/) (2017)
- [Non-Vacuous Generalisation Bounds for Shallow Neural Networks](https://mlsanity.com/paper/2202.01627/) (2022)
- [Progress in Self-Certified Neural Networks](https://mlsanity.com/paper/2111.07737/) (2021)
- [Conditionally Gaussian PAC-Bayes](https://mlsanity.com/paper/2110.11886/) (2021)
- [A Note on the Chernoff Bound for Random Variables in the Unit Interval](https://mlsanity.com/paper/2205.07880/) (2022)

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

- [Tighter PAC-Bayes Generalisation Bounds by Leveraging Example Difficulty](https://mlsanity.com/paper/2210.11289/) (2022)
- [From Privacy to Generalization: Linear Max-Information Bounds for Differentially Private Learning Algorithms](https://mlsanity.com/paper/2605.26222/) (2026)

## Abstract (arXiv)

When utilising PAC-Bayes theory for risk certification, it is usually necessary to estimate and bound the Gibbs risk of the PAC-Bayes posterior. Many works in the literature employ a method for this which requires a large number of passes of the dataset, incurring high computational cost. This manuscript presents a very general alternative which makes computational savings on the order of the dataset size.