aiqbench analysis
This is theoretical work on when leave-one-out cross-validation estimates can be trusted. It shows that estimator stability plus a gradient-growth condition yields concentration bounds, without requiring Lipschitz loss or estimator assumptions. For ML practitioners, the value is in the reasoning behind validation error guarantees for models like kernel regression, not in any new method to deploy directly.
Concentration inequalities for leave-one-out cross validation
arXiv:2211.02478v4 Announce Type: replace-cross Abstract: 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.
Abstract: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.
Statistics Theory (math.ST); Machine Learning (cs.LG); Machine Learning (stat.ML)
arXiv:2211.02478 [math.ST]
(or arXiv:2211.02478v4 [math.ST] for this version)
https://doi.org/10.48550/arXiv.2211.02478 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 193 words
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