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2020

Asymptotics of Cross-Validation

Austern, Morgane, Zhou, Wenda

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Cross validation is a central tool in evaluating the performance of machine learning and statistical models.

However, despite its ubiquitous role, its theoretical properties are still not well understood.
We study the asymptotic properties of the cross validated-risk for a large class of models.
Under stability conditions, we establish a central limit theorem and Berry-Esseen bounds, which enable us to compute asymptotically accurate confidence intervals.

Asymptotics of Cross-Validation · Around

Built on

“Beating the Hold-Out: Bounds for K-fold and Progressive Cross-Validation”
Avrim Blum, Adam Kalai and John Langford · 1999
Earlier work this paper cites.
“The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd Edition”, Springer Series in Statistics
Trevor Hastie, Robert Tibshirani and Jerome. Friedman · 2009
Earlier work this paper cites.
“Cross-Validation and Mean-Square Stability”
Satyen Kale, Ravi Kumar and Sergei Vassilvitskii · 2011
Earlier work this paper cites.

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