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Cross-validation is a popular non-parametric method for evaluating the accuracy of a predictive rule. The usefulness of cross-validation depends on the task we want to employ it for. In this note, I discuss a simple non-parametric setting,…

Methodology · Statistics 2019-09-27 Stefan Wager

Cross-validation is one of the most popular model selection methods in statistics and machine learning. Despite its wide applicability, traditional cross validation methods tend to select overfitting models, due to the ignorance of the…

Methodology · Statistics 2017-12-25 Jing Lei

Cross-validation is a widely-used technique to estimate prediction error, but its behavior is complex and not fully understood. Ideally, one would like to think that cross-validation estimates the prediction error for the model at hand, fit…

Methodology · Statistics 2024-03-12 Stephen Bates , Trevor Hastie , Robert Tibshirani

A popular data-driven method for choosing the bandwidth in standard kernel regression is cross-validation. Even when there are outliers in the data, robust kernel regression can be used to estimate the unknown regression curve [Robust and…

Statistics Theory · Mathematics 2007-06-13 Denis Heng-Yan Leung

Cross-validation (CV) is a popular approach for assessing and selecting predictive models. However, when the number of folds is large, CV suffers from a need to repeatedly refit a learning procedure on a large number of training datasets.…

Machine Learning · Statistics 2020-06-12 Ashia Wilson , Maximilian Kasy , Lester Mackey

With the increasing size of today's data sets, finding the right parameter configuration in model selection via cross-validation can be an extremely time-consuming task. In this paper we propose an improved cross-validation procedure which…

Machine Learning · Computer Science 2016-02-05 Tammo Krueger , Danny Panknin , Mikio Braun

Cross-validation (CV) methods are popular for selecting the tuning parameter in the high-dimensional variable selection problem. We show the mis-alignment of the CV is one possible reason of its over-selection behavior. To fix this issue,…

Methodology · Statistics 2018-01-17 Yang Feng , Yi Yu

Cross-validation (CV) is a common method to tune machine learning methods and can be used for model selection in regression as well. Because of the structured nature of small, traditional experimental designs, the literature has warned…

Applications · Statistics 2025-06-18 Maria L. Weese , Byran J. Smucker , David J. Edwards

We consider the problem of bandwidth selection by cross-validation from a sequential point of view in a nonparametric regression model. Having in mind that in applications one often aims at estimation, prediction and change detection…

Statistics Theory · Mathematics 2018-03-20 Ansgar Steland

Used to estimate the risk of an estimator or to perform model selection, cross-validation is a widespread strategy because of its simplicity and its apparent universality. Many results exist on the model selection performances of…

Statistics Theory · Mathematics 2011-02-01 Sylvain Arlot , Alain Celisse

We present a methodology for model evaluation and selection where the sampling mechanism violates the i.i.d. assumption. Our methodology involves a formulation of the bias between the standard Cross-Validation (CV) estimator and the mean…

Methodology · Statistics 2025-03-14 Oren Yuval , Saharon Rosset

The Maximum Likelihood (ML) and Cross Validation (CV) methods for estimating covariance hyper-parameters are compared, in the context of Kriging with a misspecified covariance structure. A two-step approach is used. First, the case of the…

Statistics Theory · Mathematics 2013-06-03 François Bachoc

Cross-validation (CV) is a technique for evaluating the ability of statistical models/learning systems based on a given data set. Despite its wide applicability, the rather heavy computational cost can prevent its use as the system size…

Machine Learning · Statistics 2016-10-26 Yoshiyuki Kabashima , Tomoyuki Obuchi , Makoto Uemura

As the main workhorse for model selection, Cross Validation (CV) has achieved an empirical success due to its simplicity and intuitiveness. However, despite its ubiquitous role, CV often falls into the following notorious dilemmas. On the…

Machine Learning · Computer Science 2020-12-29 Weikai Li , Chuanxing Geng , Songcan Chen

For linear models that may have asymmetric errors, we study variable selection by cross-validation. The data are split into training and validation sets, with the number of observations in the validation set much larger than in the training…

Methodology · Statistics 2026-01-16 Bilel Bousselmi , Gabriela Ciuperca

Cross-Validation (CV) is the default choice for evaluating the performance of machine learning models. Despite its wide usage, their statistical benefits have remained half-understood, especially in challenging nonparametric regimes. In…

Statistics Theory · Mathematics 2024-08-22 Garud Iyengar , Henry Lam , Tianyu Wang

Cross-validation (CV) is a popular method for model-selection. Unfortunately, it is not immediately obvious how to apply CV to unsupervised or exploratory contexts. This thesis discusses some extensions of cross-validation to unsupervised…

Methodology · Statistics 2009-09-17 Patrick O. Perry

Mutation validation (MV) is a recently proposed approach for model selection, garnering significant interest due to its unique characteristics and potential benefits compared to the widely used cross-validation (CV) method. In this study,…

Machine Learning · Computer Science 2024-07-25 Jinyang Yu , Sami Hamdan , Leonard Sasse , Abigail Morrison , Kaustubh R. Patil

Cross-validation (CV) is one of the most widely used techniques in statistical learning for estimating the test error of a model, but its behavior is not yet fully understood. It has been shown that standard confidence intervals for test…

Methodology · Statistics 2023-10-10 Min Woo Sun , Robert Tibshirani

Many varieties of cross validation would be statistically appealing for the estimation of smoothing and other penalized regression hyperparameters, were it not for the high cost of evaluating such criteria. Here it is shown how to…

Methodology · Statistics 2025-11-06 Simon N. Wood
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