No Unbiased Estimator of the Variance of K-Fold Cross-Validation

Part of Advances in Neural Information Processing Systems 16 (NIPS 2003)

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Yoshua Bengio, Yves Grandvalet


Most machine learning researchers perform quantitative experiments to estimate generalization error and compare algorithm performances. In order to draw statistically convincing conclusions, it is important to esti- mate the uncertainty of such estimates. This paper studies the estimation of uncertainty around the K-fold cross-validation estimator. The main theorem shows that there exists no universal unbiased estimator of the variance of K-fold cross-validation. An analysis based on the eigende- composition of the covariance matrix of errors helps to better understand the nature of the problem and shows that naive estimators may grossly underestimate variance, as con£rmed by numerical experiments.