Cross-validation Optimal Fold-Number for Model Selection

The resampling method of k-fold cross-validation is popular for error estimation and model selection in computational research. However, there is limited focus in the literature on the question of what fold number k is appropriate for various dataset dimensions. Here we review relevant literature and present a simulation of linear and least absolute shrinkage and selection operator (LASSO) regression prediction error estimation at various values of k and sample size n. In agreement with current literature, we find that contrary to a persisting understanding, there is no bias-variance trade-off in selection of k. Instead, with increasing k both bias and variance decrease, perhaps asymptotically. Our results also suggest a predictable relationship between optimal values of k and n. KEYWORDS: Cross-validation; Optimization; Fold number