# Robust Generalization via α-Mutual Information

arXiv: https://arxiv.org/abs/2001.06399 · HTML: https://mlsanity.com/paper/2001.06399/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jan 2020.

## Built on by (most cited first, 3 of 3)

- [A Survey of Robust Adversarial Training in Pattern Recognition: Fundamental, Theory, and Methodologies](https://mlsanity.com/paper/2203.14046/) (2022)
- [Deep Sufficient Representation Learning via Mutual Information](https://mlsanity.com/paper/2207.10772/) (2022)
- [PACMAN: PAC-style bounds accounting for the Mismatch between Accuracy and Negative log-loss](https://mlsanity.com/paper/2112.05547/) (2021)

## Abstract (arXiv)

The aim of this work is to provide bounds connecting two probability measures of the same event using R'enyi α-Divergences and Sibson's α-Mutual Information, a generalization of respectively the Kullback-Leibler Divergence and Shannon's Mutual Information. A particular case of interest can be found when the two probability measures considered are a joint distribution and the corresponding product of marginals (representing the statistically independent scenario). In this case, a bound using Sibson's α-Mutual Information is retrieved, extending a result involving Maximal Leakage to general alphabets. These results have broad applications, from bounding the generalization error of learning algorithms to the more general framework of adaptive data analysis, provided that the divergences and/or information measures used are amenable to such an analysis (it i.e., are robust to post-processing and compose adaptively). The generalization error bounds are derived with respect to high-probability events but a corresponding bound on expected generalization error is also retrieved.