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An important question in constructing Cross Validation (CV) estimators of the generalization error is whether rules can be established that allow "optimal" selection of the size of the training set, for fixed sample size $n$. We define the…

Statistics Theory · Mathematics 2015-11-11 Georgios Afendras , Marianthi Markatou

The growing use of model-selection principles in ecology for statistical inference is underpinned by information criteria (IC) and cross-validation (CV) techniques. Although IC techniques, such as Akaike's Information Criterion, have been…

Methodology · Statistics 2022-03-10 Luke Yates , Zach Aandahl , Shane A. Richards , Barry W. Brook

Tuning parameters in supervised learning problems are often estimated by cross-validation. The minimum value of the cross-validation error can be biased downward as an estimate of the test error at that same value of the tuning parameter.…

Applications · Statistics 2009-08-21 Ryan J. Tibshirani , 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

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

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

It is crucial to assess the predictive performance of a model to establish its practicality and relevance in real-world scenarios, particularly for high-dimensional data analysis. Among data splitting or resampling methods, cross-validation…

Methodology · Statistics 2025-11-26 Iris Ivy Gauran , Hernando Ombao , Zhaoxia Yu

We investigate generically applicable and intuitively appealing prediction intervals based on $k$-fold cross validation. We focus on the conditional coverage probability of the proposed intervals, given the observations in the training…

Statistics Theory · Mathematics 2022-05-13 Lukas Steinberger , Hannes Leeb

This paper studies generalization error bounds for Transformer models. Based on the offset Rademacher complexity, we derive sharper generalization bounds for different Transformer architectures, including single-layer single-head,…

Machine Learning · Computer Science 2026-03-24 Yawen Li , Tao Hu , Zhouhui Lian , Wan Tian , Yijie Peng , Huiming Zhang , Zhongyi Li

Cross-validation (CV) is widely used for tuning a model with respect to user-selected parameters and for selecting a "best" model. For example, the method of $k$-nearest neighbors requires the user to choose $k$, the number of neighbors,…

Applications · Statistics 2012-03-01 Hui Shen , William J. Welch , Jacqueline M. Hughes-Oliver

Minimax problems have achieved success in machine learning such as adversarial training, robust optimization, reinforcement learning. For theoretical analysis, current optimal excess risk bounds, which are composed by generalization error…

Machine Learning · Computer Science 2024-10-14 Bowei Zhu , Shaojie Li , Yong Liu

Using a support vector machine requires to set two types of hyperparameters: the soft margin parameter C and the parameters of the kernel. To perform this model selection task, the method of choice is cross-validation. Its leave-one-out…

Machine Learning · Computer Science 2008-12-18 Emmanuel Monfrini , Yann Guermeur

In machine learning one often assumes the data are independent when evaluating model performance. However, this rarely holds in practise. Geographic information data sets are an example where the data points have stronger dependencies among…

Applications · Statistics 2020-06-01 Jonne Pohjankukka , Tapio Pahikkala , Paavo Nevalainen , Jukka Heikkonen

In machine learning, statistics, econometrics and statistical physics, cross-validation (CV) is used asa standard approach in quantifying the generalisation performance of a statistical model. A directapplication of CV in time-series leads…

Machine Learning · Statistics 2021-12-14 Mehmet Süzen , Alper Yegenoglu

With machine learning being a popular topic in current computational materials science literature, creating representations for compounds has become common place. These representations are rarely compared, as evaluating their performance -…

Machine Learning · Computer Science 2023-05-26 Samantha Durdy , Michael Gaultois , Vladimir Gusev , Danushka Bollegala , Matthew J. Rosseinsky

We derive high-dimensional Gaussian comparison results for the standard $V$-fold cross-validated risk estimates. Our results combine a recent stability-based argument for the low-dimensional central limit theorem of cross-validation with…

Statistics Theory · Mathematics 2023-11-15 Nicholas Kissel , Jing Lei

We propose Rademacher complexity bounds for multiclass classifiers trained with a two-step semi-supervised model. In the first step, the algorithm partitions the partially labeled data and then identifies dense clusters containing $\kappa$…

Machine Learning · Statistics 2021-09-15 Yury Maximov , Massih-Reza Amini , Zaid Harchaoui

The selection of Gaussian kernel parameters plays an important role in the applications of support vector classification (SVC). A commonly used method is the k-fold cross validation with grid search (CV), which is extremely time-consuming…

Machine Learning · Computer Science 2025-01-22 Linkai Luo , Qiaoling Yang , Hong Peng , Yiding Wang , Ziyang Chen

We consider a priori generalization bounds developed in terms of cross-validation estimates and the stability of learners. In particular, we first derive an exponential Efron-Stein type tail inequality for the concentration of a general…

Machine Learning · Statistics 2017-06-20 Karim Abou-Moustafa , Csaba Szepesvari

Leave-one-out cross-validation (LOOCV) can be particularly accurate among cross-validation (CV) variants for machine learning assessment tasks -- e.g., assessing methods' error or variability. But it is expensive to re-fit a model $N$ times…

Machine Learning · Statistics 2020-06-24 William T. Stephenson , Tamara Broderick