Fast Computation of Nested Cross-Validation for Penalized Regression

2026-09-03

AI Summary

本文提出了一种高效计算嵌套交叉验证预测区间的方法，针对某些惩罚回归模型，只需单次模型拟合，显著减少了计算成本。

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.

Problem

• Nested Cross-Validation
• Penalized Regression
• Computational Cost

Innovation

• nested cross-validation
• penalized regression
• efficient computation