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Symbolic regression algorithms search a space of mathematical expressions for formulas that explain given data. Transformer-based models have emerged as a promising, scalable approach shifting the expensive combinatorial search to a…

Machine Learning · Computer Science 2025-09-25 Henrik Voigt , Paul Kahlmeyer , Kai Lawonn , Michael Habeck , Joachim Giesen

We revisit the problem of ensuring strong test set performance via cross-validation, and propose a nested k-fold cross-validation scheme that selects hyperparameters by minimizing a weighted sum of the usual cross-validation metric and an…

Optimization and Control · Mathematics 2026-02-04 Ryan Cory-Wright , Andrés Gómez

Developing fast regression models (surrogate/metamodels) from DEM data is key for practical industrial application to allow real-time evaluations. However, benchmarking different models is often overlooked in particle technology for…

Computational Physics · Physics 2025-09-03 B. D. Jenkins , A. L. Nicusan , A. Neveu , G. Lumay , F. Francqui , J. P. K. Seville , C. R. K. Windows-Yule

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

In traditional k-fold cross-validation, each instance is used ($k-1$) times for training and once for testing, leading to redundancy that lets many instances disproportionately influence the learning phase. We introduce Irredundant $k$-fold…

Machine Learning · Computer Science 2025-08-29 Jesus S. Aguilar-Ruiz

Cross-validation plays a fundamental role in Machine Learning, enabling robust evaluation of model performance and preventing overestimation on training and validation data. However, one of its drawbacks is the potential to create data…

Machine Learning · Computer Science 2025-08-28 Afonso Martini Spezia , Thomas Fontanari , Mariana Recamonde-Mendoza

This paper introduces e-fold cross-validation, an energy-efficient alternative to k-fold cross-validation. It dynamically adjusts the number of folds based on a stopping criterion. The criterion checks after each fold whether the standard…

Machine Learning · Computer Science 2024-10-29 Christopher Mahlich , Tobias Vente , Joeran Beel

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

State-of-the-art automated machine learning systems for tabular data often employ cross-validation; ensuring that measured performances generalize to unseen data, or that subsequent ensembling does not overfit. However, using k-fold…

Machine Learning · Computer Science 2024-08-05 Edward Bergman , Lennart Purucker , Frank Hutter

K-fold Cross Validation is commonly used to evaluate classifiers and tune their hyperparameters. However, it assumes that data points are Independent and Identically Distributed (i.i.d.) so that samples used in the training and test sets…

Machine Learning · Computer Science 2019-04-10 Akbar Dehghani , Tristan Glatard , Emad Shihab

In symbolic regression, the search for analytic models is typically driven purely by the prediction error observed on the training data samples. However, when the data samples do not sufficiently cover the input space, the prediction error…

Machine Learning · Computer Science 2020-04-28 J. Kubalík , E. Derner , R. Babuška

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

Machine learning is often applied in health science to obtain predictions and new understandings of complex phenomena and relationships, but an availability of sufficient data for model training is a widespread problem. Traditional machine…

Machine Learning · Computer Science 2021-05-18 Casper Wilstrup , Jaan Kasak

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 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 real-world problems can be naturally described by mathematical formulas. The task of finding formulas from a set of observed inputs and outputs is called symbolic regression. Recently, neural networks have been applied to symbolic…

Machine Learning · Computer Science 2022-10-24 Martin Vastl , Jonáš Kulhánek , Jiří Kubalík , Erik Derner , Robert Babuška

Common cross-validation (CV) methods like k-fold cross-validation or Monte-Carlo cross-validation estimate the predictive performance of a learner by repeatedly training it on a large portion of the given data and testing on the remaining…

Machine Learning · Computer Science 2021-11-30 Felix Mohr , Jan N. van Rijn

Cross-validation is one of the most popular model selection methods in statistics and machine learning. Despite its wide applicability, traditional cross validation methods tend to select overfitting models, due to the ignorance of the…

Methodology · Statistics 2017-12-25 Jing Lei

In the present paper, we prove a new theorem, resulting in an update formula for linear regression model residuals calculating the exact k-fold cross-validation residuals for any choice of cross-validation strategy without model refitting.…

Methodology · Statistics 2024-02-09 Kristian Hovde Liland , Joakim Skogholt , Ulf Geir Indahl

The main challenge that sets transfer learning apart from traditional supervised learning is the distribution shift, reflected as the shift between the source and target models and that between the marginal covariate distributions. In this…

Machine Learning · Statistics 2024-04-02 Zelin He , Ying Sun , Jingyuan Liu , Runze Li
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