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We study the mean-squared error of $k$-fold cross-validation as a risk estimator, with particular emphasis on how its accuracy depends on the number of folds $k$. Despite the widespread use of cross-validation, principled guidance for…

Statistics Theory · Mathematics 2026-05-26 Ido Nachum , Rüdiger Urbanke , Thomas Weinberger

Statistical machine learning models should be evaluated and validated before putting to work. Conventional k-fold Monte Carlo Cross-Validation (MCCV) procedure uses a pseudo-random sequence to partition instances into k subsets, which…

Machine Learning · Statistics 2019-07-05 Liang Guo , Jianya Liu , Ruodan Lu

The validation of modern software systems incorporates both functional and quality requirements. This paper proposes a validation approach for software quality requirement - its power consumption. This approach validates whether the…

Software Engineering · Computer Science 2007-05-23 Raimondas Lencevicius , Edu Metz , Alexander Ran

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 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

Traditionally, machine learning-based clinical prediction models have been trained and evaluated on patient data from a single source, such as a hospital. Cross-validation methods can be used to estimate the accuracy of such models on new…

Machine Learning · Computer Science 2024-10-24 Tuija Leinonen , David Wong , Antti Vasankari , Ali Wahab , Ramesh Nadarajah , Matti Kaisti , Antti Airola

Cross-validation (CV) is one of the most popular tools for assessing and selecting predictive models. However, standard CV suffers from high computational cost when the number of folds is large. Recently, under the empirical risk…

Methodology · Statistics 2023-05-30 Yuetian Luo , Zhimei Ren , Rina Foygel Barber

Over the past decades, recommendation has become a critical component of many online services such as media streaming and e-commerce. Recent advances in algorithms, evaluation methods and datasets have led to continuous improvements of the…

Information Retrieval · Computer Science 2021-11-30 Olivier Koch , Amine Benhalloum , Guillaume Genthial , Denis Kuzin , Dmitry Parfenchik

K-fold cross validation (CV) is a popular method for estimating the true performance of machine learning models, allowing model selection and parameter tuning. However, the very process of CV requires random partitioning of the data and so…

Computation and Language · Computer Science 2018-06-20 Henry B. Moss , David S. Leslie , Paul Rayson

We consider the problem of estimating the parameters of the covariance function of a Gaussian process by cross-validation. We suggest using new cross-validation criteria derived from the literature of scoring rules. We also provide an…

Computation · Statistics 2020-08-07 Sébastien Petit , Julien Bect , Sébastien da Veiga , Paul Feliot , Emmanuel Vazquez

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

In the design flow of integrated circuits, chip-level verification is an important step that sanity checks the performance is as expected. Power grid verification is one of the most expensive and time-consuming steps of chip-level…

Other Computer Science · Computer Science 2015-07-09 Jim Jing-Yan Wang , Lan Yang , Jingbin Wang , Lorenzo Azevedo

Cross-validation is a standard tool for obtaining a honest assessment of the performance of a prediction model. The commonly used version repeatedly splits data, trains the prediction model on the training set, evaluates the model…

Machine Learning · Statistics 2025-10-10 Tianyu Pan , Vincent Z. Yu , Viswanath Devanarayan , Lu Tian

Selecting learning machines such as classifiers is an important task when using AI in the clinic. K-fold crossvalidation is a practical technique that allows simple inference of such machines. However, the recipe generates many models and…

Signal Processing · Electrical Eng. & Systems 2023-01-02 Muhammad Haziq Bin Kamarul Azman , Olivier Meste , Kushsairy Kadir

We generalize fast Gaussian process leave-one-out formulae to multiple-fold cross-validation, highlighting in turn the covariance structure of cross-validation residuals in both Simple and Universal Kriging frameworks. We illustrate how…

Methodology · Statistics 2023-06-06 David Ginsbourger , Cedric Schärer

Super learner algorithm can be applied to combine results of multiple base learners to improve quality of predictions. The default method for verification of super learner results is by nested cross validation. It has been proposed by…

Machine Learning · Computer Science 2020-03-19 Krzysztof Mnich , Agnieszka Kitlas Golińska , Aneta Polewko-Klim , Witold R. Rudnicki

In the network literature, a wide range of statistical models has been proposed to exploit structural patterns in the data. Therefore, model selection between different models is a fundamental problem. However, there remains a lack of…

Methodology · Statistics 2025-08-05 Bokai Yang , Yuanxing Chen , Yuhong Yang

A common problem machine learning developers are faced with is overfitting, that is, fitting a pipeline too closely to the training data that the performance degrades for unseen data. Automated machine learning aims to free (or at least…

Machine Learning · Computer Science 2021-02-11 Benjamin Patrick Evans , Bing Xue , Mengjie Zhang

Link prediction in multilayer networks is a key challenge in applications such as recommendation systems and protein-protein interaction prediction. While many techniques have been developed, most rely on assumptions about shared structures…

Machine Learning · Statistics 2025-06-17 Yongqin Qiu , Xinyu Zhang

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