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The notion of uncertainty is of major importance in machine learning and constitutes a key element of machine learning methodology. In line with the statistical tradition, uncertainty has long been perceived as almost synonymous with…

Machine Learning · Computer Science 2021-06-24 Eyke Hüllermeier , Willem Waegeman

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

Quantifying and managing uncertainties that occur when data-driven models such as those provided by AI and machine learning methods are applied is crucial. This whitepaper provides a brief motivation and first overview of the state of the…

Machine Learning · Computer Science 2018-11-29 Michael Kläs

Quantifying the uncertainty of supervised learning models plays an important role in making more reliable predictions. Epistemic uncertainty, which usually is due to insufficient knowledge about the model, can be reduced by collecting more…

Machine Learning · Computer Science 2022-01-27 Xinlei Zhou , Han Liu , Farhad Pourpanah , Tieyong Zeng , Xizhao Wang

Due to the steadily increasing relevance of machine learning for practical applications, many of which are coming with safety requirements, the notion of uncertainty has received increasing attention in machine learning research in the last…

Machine Learning · Computer Science 2020-01-06 Mohammad Hossein Shaker , Eyke Hüllermeier

Identifying and disentangling sources of predictive uncertainty is essential for trustworthy supervised learning. We argue that widely used second-order methods that disentangle aleatoric and epistemic uncertainty are fundamentally…

Machine Learning · Computer Science 2026-02-09 Sebastián Jiménez , Mira Jürgens , Willem Waegeman

The adaptation and use of Machine Learning (ML) in our daily lives has led to concerns in lack of transparency, privacy, reliability, among others. As a result, we are seeing research in niche areas such as interpretability, causality, bias…

Machine Learning · Computer Science 2024-06-04 Fahimeh Fakour , Ali Mosleh , Ramin Ramezani

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

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

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

Recent advancements in machine learning have emphasized the need for transparency in model predictions, particularly as interpretability diminishes when using increasingly complex architectures. In this paper, we propose leveraging…

Machine Learning · Computer Science 2025-07-18 Chenrui Zhu , Louenas Bounia , Vu Linh Nguyen , Sébastien Destercke , Arthur Hoarau

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

Most machine learning techniques are based upon statistical learning theory, often simplified for the sake of computing speed. This paper is focused on the uncertainty aspect of mathematical modeling in machine learning. Regression analysis…

Machine Learning · Computer Science 2022-06-07 Valentin Arkov

Due to their increasing spread, confidence in neural network predictions became more and more important. However, basic neural networks do not deliver certainty estimates or suffer from over or under confidence. Many researchers have been…

There are two major types of uncertainty one can model. Aleatoric uncertainty captures noise inherent in the observations. On the other hand, epistemic uncertainty accounts for uncertainty in the model -- uncertainty which can be explained…

Computer Vision and Pattern Recognition · Computer Science 2017-10-06 Alex Kendall , Yarin Gal

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 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

This paper addresses a significant gap in explainable AI: the necessity of interpreting epistemic uncertainty in model explanations. Although current methods mainly focus on explaining predictions, with some including uncertainty, they fail…

Artificial Intelligence · Computer Science 2024-10-10 Helena Löfström , Tuwe Löfström , Johan Hallberg Szabadvary

Learning, whether natural or artificial, is a process of selection. It starts with a set of candidate options and selects the more successful ones. In the case of machine learning the selection is done based on empirical estimates of…

Machine Learning · Computer Science 2026-01-30 Yevgeny Seldin

In context-specific applications such as robotics, telecommunications, and healthcare, artificial intelligence systems often face the challenge of limited training data. This scarcity introduces epistemic uncertainty, i.e., reducible…

Information Theory · Computer Science 2026-03-17 Osvaldo Simeone , Yaniv Romano
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