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This article shows that increasing the observation variance at small scales can reduce the ensemble size required to avoid collapse in particle filtering of spatially-extended dynamics and improve the resulting uncertainty quantification at…

Applications · Statistics 2018-08-15 Gregor Robinson , Ian Grooms , William Kleiber

Given a fixed budget for total model size, one must choose between training a single large model or combining the predictions of multiple smaller models. We investigate this trade-off for ensembles of random-feature ridge regression models…

Machine Learning · Computer Science 2025-10-28 Benjamin S. Ruben , William L. Tong , Hamza Tahir Chaudhry , Cengiz Pehlevan

Ensemble learning has been widely recognized as a pivotal technique for boosting predictive performance by combining multiple base models. Nevertheless, conventional margin-based ensemble methods predominantly focus on maximizing the…

Machine Learning · Computer Science 2025-09-15 Zexu Jin

When randomized ensembles such as bagging or random forests are used for binary classification, the prediction error of the ensemble tends to decrease and stabilize as the number of classifiers increases. However, the precise relationship…

Probability · Mathematics 2019-05-01 Miles E. Lopes

Machine learning has emerged as a promising approach to path loss prediction, yet its effectiveness often degrades when measurement data are scarce. To address this limitation, we propose an ensemble-based machine learning framework that…

Signal Processing · Electrical Eng. & Systems 2026-05-26 Ahmed P. Mohamed , Byunghyun Lee , Yaguang Zhang , Christopher R. Anderson , David J. Love , James V. Krogmeier

Ensembling has a long history in statistical data analysis, with many impactful applications. However, in many modern machine learning settings, the benefits of ensembling are less ubiquitous and less obvious. We study, both theoretically…

Machine Learning · Statistics 2023-05-23 Ryan Theisen , Hyunsuk Kim , Yaoqing Yang , Liam Hodgkinson , Michael W. Mahoney

Accurate weather forecasting is essential for socioeconomic activities. While data-driven forecasting demonstrates superior predictive capabilities over traditional Numerical Weather Prediction (NWP) with reduced computational demands, its…

Atmospheric and Oceanic Physics · Physics 2024-12-12 Congyi Nai , Xi Chen , Shangshang Yang , Yuan Liang , Ziniu Xiao , Baoxiang Pan

The importance of accurately quantifying forecast uncertainty has motivated much recent research on probabilistic forecasting. In particular, a variety of deep learning approaches has been proposed, with forecast distributions obtained as…

Machine Learning · Statistics 2024-11-11 Benedikt Schulz , Lutz Köhler , Sebastian Lerch

Ensemble models often achieve higher accuracy than single learners, but their ability to maintain small generalization gaps is not always well understood. This study examines how ensembles balance accuracy and overfitting across four…

Machine Learning · Computer Science 2025-12-08 Zubair Ahmed Mohammad

Ensemble prediction systems are an invaluable tool for weather forecasting. Practically, ensemble predictions are obtained by running several perturbations of the deterministic control forecast. However, ensemble prediction is associated…

Machine Learning · Computer Science 2023-02-22 Rüdiger Brecht , Alex Bihlo

Multilevel Monte Carlo can efficiently compute statistical estimates of discretized random variables, for a given error tolerance. Traditionally, only a certain statistic is computed from a particular implementation of multilevel Monte…

Methodology · Statistics 2017-08-02 Alastair Gregory , Colin Cotter

Empirical evidence shows that ensembles, such as bagging, boosting, random and rotation forests, generally perform better in terms of their generalization error than individual classifiers. To explain this performance, Schapire et al.…

Machine Learning · Statistics 2019-06-10 Waldyn Martinez , J. Brian Gray

Ensemble models can be used to estimate prediction uncertainties in machine learning models. However, an ensemble of N models is approximately N times more computationally demanding compared to a single model when it is used for inference.…

Machine Learning · Computer Science 2026-03-04 Vidit Agrawal , Shixin Zhang , Lane E. Schultz , Dane Morgan

Tree-based ensemble methods such as random forests, gradient-boosted trees, and Bayesianadditive regression trees have been successfully used for regression problems in many applicationsand research studies. In this paper, we study ensemble…

Machine Learning · Statistics 2024-06-21 Alexandre Seiller , Éric Gaussier , Emilie Devijver , Marianne Clausel , Sami Alkhoury

Ensemble methods that average over a collection of independent predictors that are each limited to a subsampling of both the examples and features of the training data command a significant presence in machine learning, such as the…

Machine Learning · Statistics 2020-03-26 Daniel LeJeune , Hamid Javadi , Richard G. Baraniuk

We characterize the squared prediction risk of ensemble estimators obtained through subagging (subsample bootstrap aggregating) regularized M-estimators and construct a consistent estimator for the risk. Specifically, we consider a…

Statistics Theory · Mathematics 2025-09-30 Takuya Koriyama , Pratik Patil , Jin-Hong Du , Kai Tan , Pierre C. Bellec

Ensemble learning improves classification performance by combining multiple base classifiers. While increasing the number of classifiers generally enhances accuracy, excessively large ensembles can lead to computational inefficiency and…

Machine Learning · Computer Science 2025-11-27 Enes Bektas , Fazli Can

Predictability estimates of ensemble prediction systems are uncertain due to limited numbers of past forecasts and observations. To account for such uncertainty, this paper proposes a Bayesian inferential framework that provides a simple…

Software testing is one of the important ways to ensure the quality of software. It is found that testing cost more than 50% of overall project cost. Effective and efficient software testing utilizes the minimum resources of software.…

Machine Learning · Computer Science 2020-09-01 Ali Nawaz , Attique Ur Rehman , Muhammad Abbas

We ask the following question: what are the relative contributions of the ensemble mean and the ensemble standard deviation to the skill of a site-specific probabilistic temperature forecast? Is it the case that most of the benefit of using…

Atmospheric and Oceanic Physics · Physics 2007-05-23 Stephen Jewson