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Proper quantification of predictive uncertainty is essential for the use of machine learning in safety-critical applications. Various uncertainty measures have been proposed for this purpose, typically claiming superiority over other…

Machine Learning · Computer Science 2025-12-16 Paul Hofman , Yusuf Sale , Eyke Hüllermeier

Uncertainty representation and quantification are paramount in machine learning and constitute an important prerequisite for safety-critical applications. In this paper, we propose novel measures for the quantification of aleatoric and…

Machine Learning · Computer Science 2024-04-22 Paul Hofman , Yusuf Sale , Eyke Hüllermeier

The quantification of aleatoric and epistemic uncertainty in terms of conditional entropy and mutual information, respectively, has recently become quite common in machine learning. While the properties of these measures, which are rooted…

Machine Learning · Computer Science 2023-06-27 Lisa Wimmer , Yusuf Sale , Paul Hofman , Bern Bischl , Eyke Hüllermeier

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

Various strategies for active learning have been proposed in the machine learning literature. In uncertainty sampling, which is among the most popular approaches, the active learner sequentially queries the label of those instances for…

Machine Learning · Computer Science 2019-09-04 Vu-Linh Nguyen , Sébastien Destercke , Eyke Hüllermeier

Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the…

Numerical Analysis · Mathematics 2015-03-19 Kamaljit Chowdhary , Paul Dupuis

Quantifying uncertainty of machine learning model predictions is essential for reliable decision-making, especially in safety-critical applications. Recently, uncertainty quantification (UQ) theory has advanced significantly, building on a…

Machine Learning · Computer Science 2025-10-01 Alexander Fishkov , Kajetan Schweighofer , Mykyta Ielanskyi , Nikita Kotelevskii , Mohsen Guizani , Maxim Panov

Uncertainty quantification is at the core of the reliability and robustness of machine learning. In this paper, we provide a theoretical framework to dissect the uncertainty, especially the \textit{epistemic} component, in deep learning…

Machine Learning · Computer Science 2023-06-21 Ziyi Huang , Henry Lam , Haofeng Zhang

Uncertainty quantification has received increasing attention in machine learning in the recent past. In particular, a distinction between aleatoric and epistemic uncertainty has been found useful in this regard. The latter refers to the…

Machine Learning · Computer Science 2022-10-14 Viktor Bengs , Eyke Hüllermeier , Willem Waegeman

Regression tasks, notably in safety-critical domains, require proper uncertainty quantification, yet the literature remains largely classification-focused. In this light, we introduce a family of measures for total, aleatoric, and epistemic…

Machine Learning · Computer Science 2025-10-30 Christopher Bülte , Yusuf Sale , Gitta Kutyniok , Eyke Hüllermeier

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

In this PhD thesis, we propose a novel framework for uncertainty quantification in machine learning, which is based on proper scores. Uncertainty quantification is an important cornerstone for trustworthy and reliable machine learning…

Machine Learning · Computer Science 2025-08-26 Sebastian G. Gruber

Neural networks are ubiquitous in many tasks, but trusting their predictions is an open issue. Uncertainty quantification is required for many applications, and disentangled aleatoric and epistemic uncertainties are best. In this paper, we…

Machine Learning · Computer Science 2022-04-21 Matias Valdenegro-Toro , Daniel Saromo

It is well known that accurate probabilistic predictors can be trained through empirical risk minimisation with proper scoring rules as loss functions. While such learners capture so-called aleatoric uncertainty of predictions, various…

Machine Learning · Computer Science 2023-01-31 Viktor Bengs , Eyke Hüllermeier , Willem Waegeman

Uncertainty sampling is a prevalent active learning algorithm that queries sequentially the annotations of data samples which the current prediction model is uncertain about. However, the usage of uncertainty sampling has been largely…

Machine Learning · Computer Science 2026-04-08 Shang Liu , Xiaocheng Li

Ordinal classification problems, where labels exhibit a natural order, are prevalent in high-stakes fields such as medicine and finance. Accurate uncertainty quantification, including the decomposition into aleatoric (inherent variability)…

Machine Learning · Computer Science 2025-07-02 Stefan Haas , Eyke Hüllermeier

Uncertainty quantification is a critical aspect of machine learning models, providing important insights into the reliability of predictions and aiding the decision-making process in real-world applications. This paper proposes a novel way…

Machine Learning · Computer Science 2024-01-02 Yusuf Sale , Paul Hofman , Lisa Wimmer , Eyke Hüllermeier , Thomas Nagler

Aleatoric (data) and epistemic (knowledge) uncertainty are textbook components of Uncertainty Quantification. Jointly estimating these components has been shown to be problematic and non-trivial. As a result, there are multiple ways to…

Machine Learning · Computer Science 2026-02-12 Ivo Pascal de Jong , Andreea Ioana Sburlea , Matthia Sabatelli , Matias Valdenegro-Toro

The calibration of predictive distributions has been widely studied in deep learning, but the same cannot be said about the more specific epistemic uncertainty as produced by Deep Ensembles, Bayesian Deep Networks, or Evidential Deep…

Machine Learning · Computer Science 2024-07-18 Mohammed Fellaji , Frédéric Pennerath , Brieuc Conan-Guez , Miguel Couceiro

Applications of large language models often involve the generation of free-form responses, in which case uncertainty quantification becomes challenging. This is due to the need to identify task-specific uncertainties (e.g., about the…

Computation and Language · Computer Science 2024-10-21 Ziyu Wang , Chris Holmes
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