# An extension of McDiarmid's inequality

arXiv: https://arxiv.org/abs/1511.05240 · HTML: https://mlsanity.com/paper/1511.05240/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Nov 2015.

## Built on by (most cited first, 9 of 9)

- [Generalising realisability in statistical learning theory under epistemic uncertainty](https://mlsanity.com/paper/2402.14759/) (2024)
- [Metric Entropy-Free Sample Complexity Bounds for Sample Average Approximation in Convex Stochastic Programming](https://mlsanity.com/paper/2401.00664/) (2024)
- [Rethinking Federated Learning Over the Air: The Blessing of Scaling Up](https://mlsanity.com/paper/2508.17697/) (2025)
- [Harmful Overfitting in Sobolev Spaces](https://mlsanity.com/paper/2602.00825/) (2026)
- [Sharper Risk Bound for Multi-Task Learning with Multi-Graph Dependent Data](https://mlsanity.com/paper/2502.18167/) (2025)
- [Statistical Learning from Attribution Sets](https://mlsanity.com/paper/2602.06276/) (2026)
- [On McDiarmid's Inequality under Dependence via Approximate Tensorization of Entropy](https://mlsanity.com/paper/2606.12720/) (2026)
- [Extreme Meta-Classification for Large-Scale Zero-Shot Retrieval](https://mlsanity.com/paper/2606.25237/) (2026)
- [A Generalized McDiarmid Inequality: Sample Reuse and Non-Uniform Unbounded Differences](https://mlsanity.com/paper/2610.17159/) (2026)

## Abstract (arXiv)

We generalize McDiarmid's inequality for functions with bounded differences on a high probability set, using an extension argument. Those functions concentrate around their conditional expectations. We further extend the results to concentration in general metric spaces.