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Epistemic uncertainty in neural networks is commonly modeled using two second-order paradigms: distribution-based representations, which rely on posterior parameter distributions, and set-based representations based on credal sets (convex…

Machine Learning · Computer Science 2026-02-27 Kaizheng Wang , Yunjia Wang , Fabio Cuzzolin , David Moens , Hans Hallez , Siu Lun Chau

Uncertainty quantification is an important part of many performance critical applications. This paper provides a simple alternative to existing approaches such as ensemble learning and bayesian neural networks. By directly modeling the loss…

Machine Learning · Computer Science 2024-08-28 Yi Hung Lim

Uncertainty estimation has been widely studied in medical image segmentation as a tool to provide reliability, particularly in deep learning approaches. However, previous methods generally lack effective supervision in uncertainty…

Computer Vision and Pattern Recognition · Computer Science 2025-10-15 Yuzhu Li , An Sui , Fuping Wu , Xiahai Zhuang

Whereas confidence intervals are used to assess uncertainty due to unmeasured individuals, confounding intervals can be used to assess uncertainty due to unmeasured attributes. Previously, we have introduced a methodology for computing…

Methodology · Statistics 2025-08-13 Brian Knaeble , R Mitchell Hughes

Uncertainty quantification is a critical yet unsolved challenge for deep learning, especially for the time series imputation with irregularly sampled measurements. To tackle this problem, we propose a novel framework based on the principles…

Machine Learning · Computer Science 2023-06-05 Shweta Dahale , Sai Munikoti , Balasubramaniam Natarajan

Classification of high dimensional data finds wide-ranging applications. In many of these applications equipping the resulting classification with a measure of uncertainty may be as important as the classification itself. In this paper we…

Machine Learning · Computer Science 2018-02-12 Andrea L. Bertozzi , Xiyang Luo , Andrew M. Stuart , Konstantinos C. Zygalakis

When implementing prediction models for high-stakes real-world applications such as medicine, finance, and autonomous systems, quantifying prediction uncertainty is critical for effective risk management. Traditional approaches to…

Machine Learning · Statistics 2025-04-29 Junting Ren , Armin Schwartzman

Accurate quantification of model uncertainty has long been recognized as a fundamental requirement for trusted AI. In regression tasks, uncertainty is typically quantified using prediction intervals calibrated to an ad-hoc operating point,…

Machine Learning · Computer Science 2023-10-06 Jiri Navratil , Benjamin Elder , Matthew Arnold , Soumya Ghosh , Prasanna Sattigeri

Measurement outcomes of a quantum state can be genuinely random (unpredictable) according to the basic laws of quantum mechanics. The Heisenberg-Robertson uncertainty relation puts constrains on the accuracy of two noncommuting observables.…

Quantum Physics · Physics 2017-09-13 Xiao Yuan , Ge Bai , Tianyi Peng , Xiongfeng Ma

We gain robustness on the quantification of a risk measurement by accounting for all sources of uncertainties tainting the inputs of a computer code. We evaluate the maximum quantile over a class of distributions defined only by constraints…

Statistics Theory · Mathematics 2018-12-03 Jerome Stenger , Fabrice Gamboa , Merlin Keller , Bertrand Iooss

Deterministic mathematical models, such as those specified via differential equations, are a powerful tool to communicate scientific insight. However, such models are necessarily simplified descriptions of the real world. Generalised…

Methodology · Statistics 2025-03-24 Zheyang Shen , Jeremias Knoblauch , Sam Power , Chris. J. Oates

We present a simple comparative framework for testing and developing uncertainty modeling in uncertain marching cubes implementations. The selection of a model to represent the probability distribution of uncertain values directly…

Human-Computer Interaction · Computer Science 2024-09-16 Robert Sisneros , Tushar M. Athawale , David Pugmire , Kenneth Moreland

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 importance of uncertainty quantification is increasingly recognized in the diverse field of machine learning. Accurately assessing model prediction uncertainty can help provide deeper understanding and confidence for researchers and…

Machine Learning · Computer Science 2024-12-03 Tianyi Chen , Yingzhou Lu , Nan Hao , Yuanyuan Zhang , Capucine Van Rechem , Jintai Chen , Tianfan Fu

Artificial neural networks will always make a prediction, even when completely uncertain and regardless of the consequences. This obliviousness of uncertainty is a major obstacle towards their adoption in practice. Techniques exist,…

Machine Learning · Computer Science 2021-05-13 Hans Weytjens , Jochen De Weerdt

Data-driven forecasts of air quality have recently achieved more accurate short-term predictions. Despite their success, most of the current data-driven solutions lack proper quantifications of model uncertainty that communicate how much to…

Machine Learning · Computer Science 2021-12-07 Abdulmajid Murad , Frank Alexander Kraemer , Kerstin Bach , Gavin Taylor

The widespread adoption of machine learning surrogate models has significantly improved the scale and complexity of systems and processes that can be explored accurately and efficiently using atomistic modeling. However, the inherently…

Chemical Physics · Physics 2025-03-13 Federico Grasselli , Sanggyu Chong , Venkat Kapil , Silvia Bonfanti , Kevin Rossi

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

The practice of uncertainty quantification (UQ) validation, notably in machine learning for the physico-chemical sciences, rests on several graphical methods (scattering plots, calibration curves, reliability diagrams and confidence curves)…

Chemical Physics · Physics 2023-03-31 Pascal Pernot

Semantic segmentation is a fundamental computer vision task with a vast number of applications. State of the art methods increasingly rely on deep learning models, known to incorrectly estimate uncertainty and being overconfident in…

Computer Vision and Pattern Recognition · Computer Science 2024-07-18 Luís Almeida , Inês Dutra , Francesco Renna