Minimax Limits of k-Fold Cross-Validation via Majority
We study the mean-squared error of $k$-fold cross-validation as a risk estimator, with particular emphasis on how its accuracy depends on the number of folds $k$. Despite the widespread use of cross-validation, principled guidance for choosing $k$ is largely absent, mainly due to the complex dependence between fold-wise error estimates. To obtain sharp and interpretable results, we focus on the majority algorithm in binary classification, a minimal yet nontrivial empirical risk minimization procedure. We provide a fine-grained analysis of its cross-validation behavior, showing that even this simple algorithm exhibits subtle and delicate phenomena for which existing theory provides loose a...
| Authors | Ido Nachum, Rüdiger Urbanke, Thomas Weinberger |
|---|---|
| Primary category | math.ST |
| Published | 25 May 2026 |
| Last updated at source | 19 June 2026 |
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