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The ideas of aleatoric and epistemic uncertainty are widely used to reason about the probabilistic predictions of machine-learning models. We identify incoherence in existing discussions of these ideas and suggest this stems from the…

Machine Learning · Computer Science 2025-08-19 Freddie Bickford Smith , Jannik Kossen , Eleanor Trollope , Mark van der Wilk , Adam Foster , Tom Rainforth

Uncertainty Sampling is an Active Learning strategy that aims to improve the data efficiency of machine learning models by iteratively acquiring labels of data points with the highest uncertainty. While it has proven effective for…

Machine Learning · Computer Science 2025-02-28 Dominik Fuchsgruber , Tom Wollschläger , Bertrand Charpentier , Antonio Oroz , Stephan Günnemann

We present a novel approach to uncertainty quantification in classification tasks based on label-wise decomposition of uncertainty measures. This label-wise perspective allows uncertainty to be quantified at the individual class level,…

Machine Learning · Computer Science 2024-06-05 Yusuf Sale , Paul Hofman , Timo Löhr , Lisa Wimmer , Thomas Nagler , Eyke Hüllermeier

We address the problem of uncertainty quantification and propose measures of total, aleatoric, and epistemic uncertainty based on a known decomposition of (strictly) proper scoring rules, a specific type of loss function, into a divergence…

Machine Learning · Computer Science 2025-05-29 Paul Hofman , Yusuf Sale , Eyke Hüllermeier

Distributional data Shapley value (DShapley) has recently been proposed as a principled framework to quantify the contribution of individual datum in machine learning. DShapley develops the foundational game theory concept of Shapley values…

Machine Learning · Statistics 2021-02-19 Yongchan Kwon , Manuel A. Rivas , James Zou

In this work we show that prediction uncertainty estimates gleaned from deep learning models can be useful inputs for influencing the relative allocation of risk capital across trades. In this way, consideration of uncertainty is important…

Statistical Finance · Quantitative Finance 2020-08-03 Trent Spears , Stefan Zohren , Stephen Roberts

With the advancement of GPS, remote sensing, and computational simulations, large amounts of geospatial and spatiotemporal data are being collected at an increasing speed. Such emerging spatiotemporal big data assets, together with the…

Machine Learning · Computer Science 2024-06-24 Wenchong He , Zhe Jiang

In this paper we argue that, to its detriment, transparency research overlooks many foundational concepts of artificial intelligence. As an illustrating example we focus on uncertainty quantification in the context of counterfactual…

Machine Learning · Computer Science 2026-05-19 Kacper Sokol , Santo M. A. R. Thies , Eyke Hüllermeier

This paper tackles challenges in pricing and revenue projections due to consumer uncertainty. We propose a novel data-based approach for firms facing unknown consumer type distributions. Unlike existing methods, we assume firms only observe…

Theoretical Economics · Economics 2024-05-28 Duarte Gonçalves , Bruno A. Furtado

This paper fills the limited statistical understanding of Shapley values as a variable importance measure from a nonparametric (or smoothing) perspective. We introduce population-level \textit{Shapley curves} to measure the true variable…

Machine Learning · Statistics 2024-04-04 Ratmir Miftachov , Georg Keilbar , Wolfgang Karl Härdle

Information-theory based variational principles have proven effective at providing scalable uncertainty quantification (i.e. robustness) bounds for quantities of interest in the presence of nonparametric model-form uncertainty. In this…

Probability · Mathematics 2020-06-11 Jeremiah Birrell , Luc Rey-Bellet

U-statistics play central roles in many statistical learning tools but face the haunting issue of scalability. Significant efforts have been devoted into accelerating computation by U-statistic reduction. However, existing results almost…

Methodology · Statistics 2023-06-07 Meijia Shao , Dong Xia , Yuan Zhang

Reliable uncertainty quantification is essential for the use of machine learning in physics, where scientific discoveries depend on validated probabilistic statements. We provide a structured overview of uncertainty quantification in ML for…

Machine Learning · Statistics 2026-05-12 Manuel Haußmann , Ramon Winterhalder , Maria Ubiali

Advances in architectural design, data availability, and compute have driven remarkable progress in semantic segmentation. Yet, these models often rely on relaxed Bayesian assumptions, omitting critical uncertainty information needed for…

Computer Vision and Pattern Recognition · Computer Science 2026-02-19 M. M. A. Valiuddin , R. J. G. van Sloun , C. G. A. Viviers , P. H. N. de With , F. van der Sommen

We present a method to quantify uncertainty in the predictions made by simulations of mathematical models that can be applied to a broad class of stochastic, discrete, and differential equation models. Quantifying uncertainty is crucial for…

Machine Learning · Statistics 2015-03-05 Kyle S. Hickmann , James M. Hyman , Sara Y. Del Valle

Statistical learning algorithms provide a generally-applicable framework to sidestep time-consuming experiments, or accurate physics-based modeling, but they introduce a further source of error on top of the intrinsic limitations of the…

Chemical Physics · Physics 2024-05-17 Matthias Kellner , Michele Ceriotti

This paper introduces a comprehensive, multi-stage machine learning methodology that effectively integrates information systems and artificial intelligence to enhance decision-making processes within the domain of operations research. The…

Machine Learning · Computer Science 2023-04-14 Nijat Mehdiyev , Maxim Majlatow , Peter Fettke

The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…

Information Theory · Computer Science 2022-05-30 Kenneth Bogert

The use of high-dimensional regression techniques from machine learning has significantly improved the quantitative accuracy of interatomic potentials. Atomic simulations can now plausibly target quantitative predictions in a variety of…

Materials Science · Physics 2025-03-04 Danny Perez , Aparna P. A. Subramanyam , Ivan Maliyov , Thomas D. Swinburne

Quantification is the supervised learning task that consists of training predictors of the class prevalence values of sets of unlabelled data, and is of special interest when the labelled data on which the predictor has been trained and the…

Machine Learning · Computer Science 2023-10-10 Pablo González , Alejandro Moreo , Fabrizio Sebastiani
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