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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 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 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

Given a high-dimensional covariate matrix and a response vector, ridge-regularized sparse linear regression selects a subset of features that explains the relationship between covariates and the response in an interpretable manner. To…

Optimization and Control · Mathematics 2026-02-13 Ryan Cory-Wright , Andrés Gómez

Theoretical developments on cross validation (CV) have mainly focused on selecting one among a list of finite-dimensional models (e.g., subset or order selection in linear regression) or selecting a smoothing parameter (e.g., bandwidth for…

Statistics Theory · Mathematics 2008-12-18 Yuhong Yang

Cross validation is commonly used for selecting tuning parameters in penalized regression, but its use in penalized Cox regression models has received relatively little attention in the literature. Due to its partial likelihood…

Methodology · Statistics 2026-05-13 Biyue Dai , Patrick Breheny

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

Cross-validation is frequently used for model selection in a variety of applications. However, it is difficult to apply cross-validation to mixed effects models (including nonlinear mixed effects models or NLME models) due to the fact that…

Methodology · Statistics 2013-05-24 Emily Colby , Eric Bair

In this paper, we develop an implementation of cross-validation for penalized linear mixed models. While these models have been proposed for correlated high-dimensional data, the current literature implicitly assumes that tuning parameter…

Methodology · Statistics 2025-03-19 Tabitha K. Peter , Patrick J. Breheny

When selecting a classification algorithm to be applied to a particular problem, one has to simultaneously select the best algorithm for that dataset \emph{and} the best set of hyperparameters for the chosen model. The usual approach is to…

Machine Learning · Computer Science 2018-09-26 Jacques Wainer , Gavin Cawley

Cross-validation is a widely used technique for evaluating the performance of prediction models, ranging from simple binary classification to complex precision medicine strategies. It helps correct for optimism bias in error estimates,…

In this paper, for Lasso penalized linear regression models in high-dimensional settings, we propose a modified cross-validation method for selecting the penalty parameter. The methodology is extended to other penalties, such as Elastic…

Methodology · Statistics 2013-09-10 Yi Yu , Yang Feng

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 is the standard approach for tuning parameter selection in many non-parametric regression problems. However its use is less common in change-point regression, perhaps as its prediction error-based criterion may appear to…

Methodology · Statistics 2024-02-13 Florian Pein , Rajen D. Shah

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

Cross-validation is the de facto standard for predictive model evaluation and selection. In proper use, it provides an unbiased estimate of a model's predictive performance. However, data sets often undergo various forms of data-dependent…

Methodology · Statistics 2023-01-18 Amit Moscovich , Saharon Rosset

We introduce a novel procedure for obtaining cross-validated predictive estimates for Bayesian hierarchical regression models (BHRMs). Bayesian hierarchical models are popular for their ability to model complex dependence structures and…

Machine Learning · Statistics 2024-10-01 Amy X. Zhang , Le Bao , Changcheng Li , Michael J. Daniels

Cross validation is widely used for selecting tuning parameters in regularization methods, but it is computationally intensive in general. To lessen its computational burden, approximation schemes such as generalized approximate cross…

Methodology · Statistics 2024-12-02 Shanshan Tu , Yunzhang Zhu , Yoonkyung Lee , Qiuyu Gu , Haozhen Yu

This text is a survey on cross-validation. We define all classical cross-validation procedures, and we study their properties for two different goals: estimating the risk of a given estimator, and selecting the best estimator among a given…

Statistics Theory · Mathematics 2017-03-10 Sylvain Arlot

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
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