Concentration inequalities for leave-one-out cross validation
Statistics Theory
2023-10-17 v3 Machine Learning
Machine Learning
Statistics Theory
Abstract
In this article we prove that estimator stability is enough to show that leave-one-out cross validation is a sound procedure, by providing concentration bounds 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.
Cite
@article{arxiv.2211.02478,
title = {Concentration inequalities for leave-one-out cross validation},
author = {Benny Avelin and Lauri Viitasaari},
journal= {arXiv preprint arXiv:2211.02478},
year = {2023}
}