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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

The future predictive performance of a Bayesian model can be estimated using Bayesian cross-validation. In this article, we consider Gaussian latent variable models where the integration over the latent values is approximated using the…

Computation · Statistics 2016-08-09 Aki Vehtari , Tommi Mononen , Ville Tolvanen , Tuomas Sivula , Ole Winther

In this article we prove that estimator stability is enough to show that leave-one-out cross validation is a sound procedure, by providing concentration bounds in a general framework. In particular, we provide concentration bounds beyond…

Statistics Theory · Mathematics 2023-10-17 Benny Avelin , Lauri Viitasaari

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

Conditional independence testing is an important problem, yet provably hard without assumptions. One of the assumptions that has become popular of late is called "model-X", where we assume we know the joint distribution of the covariates,…

Methodology · Statistics 2020-07-14 Eugene Katsevich , Aaditya Ramdas

Model overconfidence and poor calibration are common in machine learning and difficult to account for when applying standard empirical risk minimization. In this work, we propose a novel method to alleviate these problems that we call…

Machine Learning · Computer Science 2024-02-13 Lukas Muttenthaler , Robert A. Vandermeulen , Qiuyi Zhang , Thomas Unterthiner , Klaus-Robert Müller

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

Consider the following class of learning schemes: \begin{equation} \label{eq:main-problem1} \hat{\boldsymbol{\beta}} := \underset{\boldsymbol{\beta} \in \mathcal{C}}{\arg\min} \;\sum_{j=1}^n \ell(\boldsymbol{x}_j^\top\boldsymbol{\beta};…

Machine Learning · Computer Science 2018-10-08 Shuaiwen Wang , Wenda Zhou , Arian Maleki , Haihao Lu , Vahab Mirrokni

We study prediction intervals based on leave-one-out residuals in a linear regression model where the number of explanatory variables can be large compared to sample size. We establish uniform asymptotic validity (conditional on the…

Statistics Theory · Mathematics 2016-02-19 Lukas Steinberger , Hannes Leeb

This article introduces a leave-one-out regression adjustment (LOORA) for estimating average treatment effects in randomized controlled trials. In finite samples, LOORA removes the bias of conventional regression adjustment and yields exact…

Econometrics · Economics 2026-05-08 Alberto Abadie , Mehrdad Ghadiri , Ali Jadbabaie , Mahyar JafariNodeh

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

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

The asymptotic optimality (a.o.) of various hyper-parameter estimators with different optimality criteria has been studied in the literature for regularized least squares regression problems. The estimators include e.g., the maximum…

Statistics Theory · Mathematics 2021-04-28 Biqiang Mu , Tianshi Chen , Lennart Ljung

A data analyst might worry about generalization if dropping a very small fraction of data points from a study could change its substantive conclusions. Checking this non-robustness directly poses a combinatorial optimization problem and is…

Methodology · Statistics 2025-09-10 Jenny Y. Huang , David R. Burt , Yunyi Shen , Tin D. Nguyen , Tamara Broderick

This paper proposed a new regression model called $l_1$-regularized outlier isolation and regression (LOIRE) and a fast algorithm based on block coordinate descent to solve this model. Besides, assuming outliers are gross errors following a…

Computer Vision and Pattern Recognition · Computer Science 2014-11-21 Sheng Han , Suzhen Wang , Xinyu Wu

Variance estimation in the linear model when $p > n$ is a difficult problem. Standard least squares estimation techniques do not apply. Several variance estimators have been proposed in the literature, all with accompanying asymptotic…

Methodology · Statistics 2014-01-30 Stephen Reid , Robert Tibshirani , Jerome Friedman

This paper investigates the estimation problem in a regression-type model. To be able to deal with potential high dimensions, we provide a procedure called LOL, for Learning Out of Leaders with no optimization step. LOL is an auto-driven…

Statistics Theory · Mathematics 2011-01-24 Mathilde Mougeot , Dominique Picard , Karine Tribouley

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

Ordinary least squares (OLS) linear regression is one of the most basic statistical techniques for data analysis. In the main stream literature and the statistical education, the study of linear regression is typically restricted to the…

Statistics Theory · Mathematics 2018-09-28 Arun K. Kuchibhotla , Lawrence D. Brown , Andreas Buja

An important issue in many multivariate regression problems is to eliminate candidate predictors with null predictor vectors. In large-dimensional (LD) setting where the numbers of responses and predictors are large, model selection…

Statistics Theory · Mathematics 2023-04-26 Zhidong Bai , Kwok Pui Choi , Yasunori Fujikoshi , Jiang Hu