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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

Modelling uncertainty in Machine Learning models is essential for achieving safe and reliable predictions. Most research on uncertainty focuses on output uncertainty (predictions), but minimal attention is paid to uncertainty at inputs. We…

Machine Learning · Computer Science 2024-06-28 Matias Valdenegro-Toro , Ivo Pascal de Jong , Marco Zullich

Machine learning is central to empirical asset pricing, but portfolio construction still relies on point predictions and largely ignores asset-specific estimation uncertainty. We propose a simple change: sort assets using…

Portfolio Management · Quantitative Finance 2026-01-05 Yan Liu , Ye Luo , Zigan Wang , Xiaowei Zhang

Despite AI's impressive achievements, including recent advances in generative and large language models, there remains a significant gap in the ability of AI systems to handle uncertainty and generalize beyond their training data. AI models…

Artificial Intelligence · Computer Science 2025-06-30 Shireen Kudukkil Manchingal , Andrew Bradley , Julian F. P. Kooij , Keivan Shariatmadar , Neil Yorke-Smith , Fabio Cuzzolin

In machine learning, accurately predicting the probability that a specific input is correct is crucial for risk management. This process, known as uncertainty (or confidence) estimation, is particularly important in mission-critical…

Machine Learning · Computer Science 2023-01-12 Gabriella Chouraqui , Liron Cohen , Gil Einziger , Liel Leman

Model selection is a necessary step in unsupervised machine learning. Despite numerous criteria and metrics, model selection remains subjective. A high degree of subjectivity may lead to questions about repeatability and reproducibility of…

Machine Learning · Computer Science 2024-01-08 Wanyi Chen , Mary L. Cummings

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

Stochastic dominance serves as a general framework for modeling a broad spectrum of decision preferences under uncertainty, with risk aversion as one notable example, as it naturally captures the intrinsic structure of the underlying…

Machine Learning · Computer Science 2026-01-06 Shicong Cen , Jincheng Mei , Hanjun Dai , Dale Schuurmans , Yuejie Chi , Bo Dai

Building on the view of machine learning as search, we demonstrate the necessity of bias in learning, quantifying the role of bias (measured relative to a collection of possible datasets, or more generally, information resources) in…

Machine Learning · Computer Science 2019-07-16 George D. Montanez , Jonathan Hayase , Julius Lauw , Dominique Macias , Akshay Trikha , Julia Vendemiatti

With the wide adoption of machine learning techniques, requirements have evolved beyond sheer high performance, often requiring models to be trustworthy. A common approach to increase the trustworthiness of such systems is to allow them to…

Machine Learning · Computer Science 2023-11-16 Andrea Pugnana , Carlos Mougan , Dan Saattrup Nielsen

This paper reviews recent advances in the field of optimization under uncertainty via a modern data lens, highlights key research challenges and promise of data-driven optimization that organically integrates machine learning and…

Machine Learning · Computer Science 2019-04-16 Chao Ning , Fengqi You

Machine learning is the science of discovering statistical dependencies in data, and the use of those dependencies to perform predictions. During the last decade, machine learning has made spectacular progress, surpassing human performance…

Machine Learning · Statistics 2016-07-13 David Lopez-Paz

As neural networks become more popular, the need for accompanying uncertainty estimates increases. There are currently two main approaches to test the quality of these estimates. Most methods output a density. They can be compared by…

Machine Learning · Statistics 2024-06-05 Laurens Sluijterman , Eric Cator , Tom Heskes

Uncertainty quantification is a key pillar of trustworthy machine learning. It enables safe reactions under unsafe inputs, like predicting only when the machine learning model detects sufficient evidence, discarding anomalous data, or…

Machine Learning · Computer Science 2024-08-27 Michael Kirchhof

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

We consider a simulation-based Ranking and Selection (R&S) problem with input uncertainty, where unknown input distributions can be estimated using input data arriving in batches of varying sizes over time. Each time a batch arrives,…

Optimization and Control · Mathematics 2022-09-05 Di Wu , Yuhao Wang , Enlu Zhou

Targeted Learning is a subfield of statistics that unifies advances in causal inference, machine learning and statistical theory to help answer scientifically impactful questions with statistical confidence. Targeted Learning is driven by…

Deep learning has emerged as a promising paradigm to give access to highly accurate predictions of molecular and materials properties. A common short-coming shared by current approaches, however, is that neural networks only give point…

Computational Physics · Physics 2023-05-10 Albert Zhu , Simon Batzner , Albert Musaelian , Boris Kozinsky

Learning and decision-making in domains with naturally high noise-to-signal ratio, such as Finance or Healthcare, is often challenging, while the stakes are very high. In this paper, we study the problem of learning and acting under a…

Machine Learning · Computer Science 2023-09-26 Yikai Zhang , Songzhu Zheng , Mina Dalirrooyfard , Pengxiang Wu , Anderson Schneider , Anant Raj , Yuriy Nevmyvaka , Chao Chen

Machine learning models have emerged as a very effective strategy to sidestep time-consuming electronic-structure calculations, enabling accurate simulations of greater size, time scale and complexity. Given the interpolative nature of…