Cross-validation Confidence Intervals for Test Error

Pierre Bayle; Alexandre Bayle; Lucas Janson; Lester Mackey

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arXiv · 2007.12671

Cross-validation Confidence Intervals for Test Error

Pierre Bayle·Alexandre Bayle·Lucas Janson·Lester Mackey

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Abstract

This work develops central limit theorems for cross-validation and consistent estimators of its asymptotic variance under weak stability conditions on the learning algorithm. Together, these results provide practical, asymptotically-exact confidence intervals for $k$-fold test error and valid, powerful hypothesis tests of whether one learning algorithm has smaller $k$-fold test error than another. These results are also the first of their kind for the popular choice of leave-one-out cross-validation. In our real-data experiments with diverse learning algorithms, the resulting intervals and tests outperform the most popular alternative methods from the literature.

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BibTeX RIS

Pierre Bayle, Alexandre Bayle, Lucas Janson, Lester Mackey. 2020-07-24. Cross-validation Confidence Intervals for Test Error. https://arxiv.org/abs/2007.12671

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