Algorithmic Stability and Sanity-Check Bounds for Leave-One-Out Cross-Validation

摘要

In this article we prove sanity-check bounds for the error of the leave-one- out cross-validation estimate of the generalization error: that is, bounds showing that the worst-case error of this estimate is not much worse than that of the training error estimate. The name sanity check refers to the fact that although we often expect the leave-one-out estimate to perform considerably better than the training error estimate, we are here only seeking assurance that the training error estimate, we are here only seeking assurance that its performance will not be considerably worse. Perhaps surprisingly, such assurance has been given only for limited cases In the prior literature on cross-validation.