Fast Computation of Nested Cross-Validation for Penalized Regression
Abstract
Cross-validation is a resampling procedure that provides a point estimate of generalization error for any predictive model. Cross-validation is widely used for model selection and evaluation. Uncertainty in the cross-validation estimate is challenging to quantify, and estimation of its variance is known to require multiple runs of the entire resampling procedure. Nested cross-validation computes a prediction interval for the generalization error for a given model and training dataset by resampling the entire cross-validation procedure but incurs extraordinary computational cost. We provide an efficient method for computing the nested cross-validation prediction interval using only a single model fit for some penalized regression models including ridge regression, spline smoothing, and some functional regression models. We characterize when our proposed method should be expected to out-perform resampling-based nested cross-validation in various scaling regimes as well as in finite samples. Experiments for functional principle components regression demonstrate non-trivial cases in which our proposed method improves run times substantially.
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BibTeX
@misc{cao2026fast,
title = {{Fast Computation of Nested Cross-Validation for Penalized Regression}},
author = {Shuyang Cao and Alex Stringer},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04126},
eprint = {2609.04126},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04126},
}
RIS
TY - UNPB
TI - Fast Computation of Nested Cross-Validation for Penalized Regression
AU - Shuyang Cao
AU - Alex Stringer
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.04126
UR - https://arxiv.org/abs/2609.04126
AB - Cross-validation is a resampling procedure that provides a point estimate of generalization error for any predictive model. Cross-validation is widely used for model selection and evaluation. Uncertainty in the cross-validation estimate is challenging to quantify, and estimation of its variance is known to require multiple runs of the entire resampling procedure. Nested cross-validation computes a prediction interval for the generalization error for a given model and training dataset by resampling the entire cross-validation procedure but incurs extraordinary computational cost. We provide an efficient method for computing the nested cross-validation prediction interval using only a single model fit for some penalized regression models including ridge regression, spline smoothing, and some functional regression models. We characterize when our proposed method should be expected to out-perform resampling-based nested cross-validation in various scaling regimes as well as in finite samples. Experiments for functional principle components regression demonstrate non-trivial cases in which our proposed method improves run times substantially.
ER -