# Concentration inequalities for leave-one-out cross validation

arXiv: https://arxiv.org/abs/2211.02478 · HTML: https://mlsanity.com/paper/2211.02478/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 40 references that are in the map.
- First posted on arXiv 4 Nov 2022.

## Builds on (most cited first, 3 of 3)

- [Cross-validation: what does it estimate and how well does it do it?](https://mlsanity.com/paper/2104.00673/) (2021)
- [Stability revisited: new generalisation bounds for the Leave-one-Out](https://mlsanity.com/paper/1608.06412/) (2016)
- [An Exponential Efron-Stein Inequality for Lq Stable Learning Rules](https://mlsanity.com/paper/1903.05457/) (2019)

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

- [Failures and Successes of Cross-Validation for Early-Stopped Gradient Descent](https://mlsanity.com/paper/2402.16793/) (2024)
- [Distributional bias compromises leave-one-out cross-validation](https://mlsanity.com/paper/2406.01652/) (2024)
- [Estimating Population-Risk Curves Along Nonconvex Gradient Flows from the Training Sample](https://mlsanity.com/paper/2608.30261/) (2026)

## Abstract (arXiv)

In this article we prove that estimator stability, together with a gradient-growth condition on the expected fitted loss, is enough to provide concentration bounds for leave-one-out cross-validation in a general framework. In particular, we provide concentration bounds beyond Lipschitz continuity assumptions on the loss or on the estimator. We obtain our results by relying on random variables with distribution satisfying the logarithmic Sobolev inequality, providing us a relatively rich class of distributions. We illustrate our method by considering several interesting examples, including linear regression, kernel density estimation, and stabilized/truncated estimators such as stabilized kernel regression.