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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

While many statistical models and methods are now available for network analysis, resampling network data remains a challenging problem. Cross-validation is a useful general tool for model selection and parameter tuning, but is not directly…

Methodology · Statistics 2020-05-04 Tianxi Li , Elizaveta Levina , Ji Zhu

Neural networks are among the most powerful nonlinear models used to address supervised learning problems. Similar to most machine learning algorithms, neural networks produce point predictions and do not provide any prediction interval…

Machine Learning · Statistics 2020-07-01 Saeed Khaki , Dan Nettleton

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,…

K-fold cross-validation (CV) with squared error loss is widely used for evaluating predictive models, especially when strong distributional assumptions cannot be taken. However, CV with squared error loss is not free from distributional…

Methodology · Statistics 2021-08-10 Assaf Rabinowicz , Saharon Rosset

With the increasing size of today's data sets, finding the right parameter configuration in model selection via cross-validation can be an extremely time-consuming task. In this paper we propose an improved cross-validation procedure which…

Machine Learning · Computer Science 2016-02-05 Tammo Krueger , Danny Panknin , Mikio Braun

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

Group number selection is a key problem for group panel data modeling. In this work, we develop a cross-validation (CV) method to tackle this problem. Specifically, we split the panel data into two data folds on the time span, with group…

Methodology · Statistics 2025-05-19 Zhe Li , Xuening Zhu , Changliang Zou

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

We discuss systematically two versions of confidence regions: those based on p-values and those based on e-values, a recent alternative to p-values. Both versions can be applied to multiple hypothesis testing, and in this paper we are…

Statistics Theory · Mathematics 2024-03-05 Vladimir Vovk , Ruodu Wang

Despite the extensive literature on training loss functions, the evaluation of generalization on the validation set remains underexplored. In this work, we conduct a systematic empirical and statistical study of how the validation criterion…

Machine Learning · Computer Science 2026-02-26 Andrea Apicella , Francesco Isgrò , Andrea Pollastro , Roberto Prevete

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

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

Electronic exams (e-exams) have the potential to substantially reduce the effort required for conducting an exam through automation. Yet, care must be taken to sacrifice neither task complexity nor constructive alignment nor grading…

Computers and Society · Computer Science 2023-08-17 Ole Lübke , Konrad Fuger , Fin Hendrik Bahnsen , Katrin Billerbeck , Sibylle Schupp

Complex and larger networks are becoming increasingly prevalent in scientific applications in various domains. Although a number of models and methods exist for such networks, cross-validation on networks remains challenging due to the…

Methodology · Statistics 2026-03-12 Sayan Chakrabarty , Srijan Sengupta , Yuguo Chen

Model selection is a crucial issue in machine-learning and a wide variety of penalisation methods (with possibly data dependent complexity penalties) have recently been introduced for this purpose. However their empirical performance is…

Machine Learning · Statistics 2012-12-11 Charanpal Dhanjal , Nicolas Baskiotis , Stéphan Clémençon , Nicolas Usunier

Cross-validation is a statistical tool that can be used to improve large covariance matrix estimation. Although its efficiency is observed in practical applications and a convergence result towards the error of the non linear shrinkage is…

Statistics Theory · Mathematics 2025-09-18 Lamia Lamrani , Christian Bongiorno , Marc Potters

In many real-world applications of machine learning, we are interested to know if it is possible to train on the data that we have gathered so far, and obtain accurate predictions on a new test data subset that is qualitatively different in…

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

This paper discusses a counterpart of conformal prediction for e-values, conformal e-prediction. Conformal e-prediction is conceptually simpler and had been developed in the 1990s as a precursor of conformal prediction. When conformal…

Machine Learning · Computer Science 2025-05-20 Vladimir Vovk