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In this article we prove that estimator stability is enough to show thatleave-one-out cross validation is a sound procedure, by providing concentrationbounds in a general framework. In particular, we provide concentration boundsbeyond Lipschitz continuity assumptions on the loss or on the estimator. Weobtain our results by relying on random variables with distribution satisfyingthe logarithmic Sobolev inequality, providing us a relatively rich class ofdistributions. We illustrate our method by considering several interestingexamples, including linear regression, kernel density estimation, andstabilized/truncated estimators such as stabilized kernel regression.

Concentration inequalities for leave-one-out cross validation