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It is useful to estimate the expected predictive performance of models planned to be used for prediction. We focus on leave-one-out cross-validation (LOO-CV), which has become a popular method for estimating predictive performance of…

Methodology · Statistics 2025-10-29 Tuomas Sivula , Måns Magnusson , Asael Alonzo Matamoros , Aki Vehtari

Evaluating the predictive performance of a statistical model is commonly done using cross-validation. Among the various methods, leave-one-out cross-validation (LOOCV) is frequently used. Originally designed for exchangeable observations,…

Computation · Statistics 2025-07-04 Zhedong Liu , Janet Van Niekerk , Haavard Rue

In this paper, we derive non-asymptotic error bounds for the Lasso estimator when the penalty parameter for the estimator is chosen using $K$-fold cross-validation. Our bounds imply that the cross-validated Lasso estimator has nearly…

Statistics Theory · Mathematics 2020-02-07 Denis Chetverikov , Zhipeng Liao , Victor Chernozhukov

We analyze the performance of cross-validation (CV) in the density estimation framework with two purposes: (i) risk estimation and (ii) model selection. The main focus is given to the so-called leave-$p$-out CV procedure (Lpo), where $p$…

Statistics Theory · Mathematics 2014-10-02 Alain Celisse

The present work aims at deriving theoretical guaranties on the behavior of some cross-validation procedures applied to the $k$-nearest neighbors ($k$NN) rule in the context of binary classification. Here we focus on the leave-$p$-out…

Statistics Theory · Mathematics 2017-10-13 Alain Celisse , Tristan Mary-Huard

Cross-validation is a common method for estimating the predictive performance of machine learning models. In a data-scarce regime, where one typically wishes to maximize the number of instances used for training the model, an approach…

Methodology · Statistics 2025-03-25 George I. Austin , Itsik Pe'er , Tal Korem

We conduct a non asymptotic study of the Cross Validation (CV) estimate of the generalization risk for learning algorithms dedicated to extreme regions of the covariates space. In this Extreme Value Analysis context, the risk function…

Statistics Theory · Mathematics 2024-09-12 Anass Aghbalou , Patrice Bertail , François Portier , Anne Sabourin

We investigate leave-one-out cross validation (CV) as a determinator of the weight of the penalty term in the least absolute shrinkage and selection operator (LASSO). First, on the basis of the message passing algorithm and a perturbative…

Information Theory · Computer Science 2016-06-22 Tomoyuki Obuchi , Yoshiyuki Kabashima

Despite the tremendous empirical success of deep learning models to solve various learning tasks, our theoretical understanding of their generalization ability is very limited. Classical generalization bounds based on tools such as the VC…

Machine Learning · Computer Science 2022-03-08 Gregor Bachmann , Thomas Hofmann , Aurélien Lucchi

One of the common goals of time series analysis is to use the observed series to inform predictions for future observations. In the absence of any actual new data to predict, cross-validation can be used to estimate a model's future…

Methodology · Statistics 2020-07-02 Paul-Christian Bürkner , Jonah Gabry , Aki Vehtari

Comparison of competing statistical models is an essential part of psychological research. From a Bayesian perspective, various approaches to model comparison and selection have been proposed in the literature. However, the applicability of…

Applications · Statistics 2020-05-28 Riko Kelter

This paper examines LASSO, a widely-used $L_{1}$-penalized regression method, in high dimensional linear predictive regressions, particularly when the number of potential predictors exceeds the sample size and numerous unit root regressors…

Econometrics · Economics 2024-01-17 Ziwei Mei , Zhentao Shi

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

Leave-one-out (LOO) prediction provides a principled, data-dependent measure of generalization, yet guarantees in fully transductive settings remain poorly understood beyond specialized models. We introduce Median of Level-Set Aggregation…

Machine Learning · Computer Science 2026-03-03 Jian Qian , Jiachen Xu

We consider linear regression in the high-dimensional regime where the number of observations $n$ is smaller than the number of parameters $p$. A very successful approach in this setting uses $\ell_1$-penalized least squares (a.k.a. the…

Methodology · Statistics 2014-02-05 Adel Javanmard , Andrea Montanari

High-dimensional predictive models, those with more measurements than observations, require regularization to be well defined, perform well empirically, and possess theoretical guarantees. The amount of regularization, often determined by…

Methodology · Statistics 2019-07-16 Darren Homrighausen , Daniel J. McDonald

In recent decades, multilevel regression and poststratification (MRP) has surged in popularity for population inference. However, the validity of the estimates can depend on details of the model, and there is currently little research on…

Methodology · Statistics 2022-09-07 Swen Kuh , Lauren Kennedy , Qixuan Chen , Andrew Gelman

Two key tasks in high-dimensional regularized regression are tuning the regularization strength for accurate predictions and estimating the out-of-sample risk. It is known that the standard approach -- $k$-fold cross-validation -- is…

Statistics Theory · Mathematics 2025-10-24 Kevin Luo , Yufan Li , Pragya Sur

Leave-one-out cross-validation (LOO) and the widely applicable information criterion (WAIC) are methods for estimating pointwise out-of-sample prediction accuracy from a fitted Bayesian model using the log-likelihood evaluated at the…

Computation · Statistics 2017-12-18 Aki Vehtari , Andrew Gelman , Jonah Gabry

A generic out-of-sample error estimate is proposed for robust $M$-estimators regularized with a convex penalty in high-dimensional linear regression where $(X,y)$ is observed and $p,n$ are of the same order. If $\psi$ is the derivative of…

Statistics Theory · Mathematics 2023-03-31 Pierre C Bellec