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This article expands the framework of Bayesian inference and provides direct probabilistic methods for approaching inference tasks that are typically handled with information theory. We treat Bayesian probability updating as a random…

Data Analysis, Statistics and Probability · Physics 2023-11-20 Kevin Vanslette

We consider the problem of performing Bayesian inference in probabilistic models where observations are accompanied by uncertainty, referred to as "uncertain evidence." We explore how to interpret uncertain evidence, and by extension the…

Machine Learning · Statistics 2023-01-27 Andreas Munk , Alexander Mead , Frank Wood

We introduce a novel uncertainty estimation for classification tasks for Bayesian convolutional neural networks with variational inference. By normalizing the output of a Softplus function in the final layer, we estimate aleatoric and…

Machine Learning · Computer Science 2019-05-15 Kumar Shridhar , Felix Laumann , Marcus Liwicki

Decomposing predictive uncertainty into epistemic (model ignorance) and aleatoric (data ambiguity) components is central to reliable decision making, yet most methods estimate both from the same predictive distribution. Recent empirical and…

Machine Learning · Computer Science 2026-02-13 Tanmoy Mukherjee , Marius Kloft , Pierre Marquis , Zied Bouraoui

The ability to acknowledge the inevitable uncertainty in their knowledge and reasoning is a prerequisite for AI systems to be truly truthful and reliable. In this paper, we present a taxonomy of uncertainty specific to vision-language AI…

Artificial Intelligence · Computer Science 2024-07-03 Khyathi Raghavi Chandu , Linjie Li , Anas Awadalla , Ximing Lu , Jae Sung Park , Jack Hessel , Lijuan Wang , Yejin Choi

A Bayesian treatment of deep learning allows for the computation of uncertainties associated with the predictions of deep neural networks. We show how the concept of Errors-in-Variables can be used in Bayesian deep regression to also…

Machine Learning · Computer Science 2023-05-15 Jörg Martin , Clemens Elster

Supervised machine learning and predictive models have achieved an impressive standard today, enabling us to answer questions that were inconceivable a few years ago. Besides these successes, it becomes clear, that beyond pure prediction,…

Machine Learning · Statistics 2025-01-29 Cornelia Gruber , Patrick Oliver Schenk , Malte Schierholz , Frauke Kreuter , Göran Kauermann

Due to their intuitive appeal, Bayesian methods of modeling and uncertainty quantification have become popular in modern machine and deep learning. When providing a prior distribution over the parameter space, it is straightforward to…

Machine Learning · Statistics 2025-06-05 Ivan Melev , Goeran Kauermann

Quantifying model uncertainty is critical for understanding prediction reliability, yet distinguishing between aleatoric and epistemic uncertainty remains challenging. We extend recent work from classification to regression to provide a…

We develop a new framework of uncertainty variables to model uncertainty. An uncertainty variable is characterized by an uncertainty set, in which its realization is bound to lie, while the conditional uncertainty is characterized by a set…

Machine Learning · Statistics 2019-12-10 Rajat Talak , Sertac Karaman , Eytan Modiano

Information theory provides a mathematical foundation to measure uncertainty in belief. Belief is represented by a probability distribution that captures our understanding of an outcome's plausibility. Information measures based on…

Information Theory · Computer Science 2020-01-17 Jed A. Duersch , Thomas A. Catanach

Inverse Uncertainty Quantification (UQ), or Bayesian calibration, is the process to quantify the uncertainties of random input parameters based on experimental data. The introduction of model discrepancy term is significant because…

Applications · Statistics 2019-07-24 Xu Wu , Koroush Shirvan , Tomasz Kozlowski

Researchers in explainable artificial intelligence have developed numerous methods for helping users understand the predictions of complex supervised learning models. By contrast, explaining the $\textit{uncertainty}$ of model outputs has…

Machine Learning · Statistics 2023-11-01 David S. Watson , Joshua O'Hara , Niek Tax , Richard Mudd , Ido Guy

Data-driven control in unknown environments requires a clear understanding of the involved uncertainties for ensuring safety and efficient exploration. While aleatoric uncertainty that arises from measurement noise can often be explicitly…

Machine Learning · Computer Science 2023-07-13 Neha Das , Jonas Umlauft , Armin Lederer , Thomas Beckers , Sandra Hirche

In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…

Machine Learning · Computer Science 2019-04-03 Konstantin Posch , Jürgen Pilz

Uncertainty estimation is pivotal in machine learning, especially for classification tasks, as it improves the robustness and reliability of models. We introduce a novel `Epistemic Wrapping' methodology aimed at improving uncertainty…

Statistical tools of uncertainty quantification can be used to assess the information content of measured observables with respect to present-day theoretical models; to estimate model errors and thereby improve predictive capability; to…

Nuclear Theory · Physics 2015-03-26 J. D. McDonnell , N. Schunck , D. Higdon , J. Sarich , S. M. Wild , W. Nazarewicz

There are two reasons why uncertainty may not be adequately described by Probability Theory. The first one is due to unique or nearly-unique events, that either never realized or occurred too seldom for frequencies to be reliably measured.…

Artificial Intelligence · Computer Science 2023-03-17 Florian Ellsaesser , Guido Fioretti , Gail E. James

Epistemic Uncertainty is a measure of the lack of knowledge of a learner which diminishes with more evidence. While existing work focuses on using the variance of the Bayesian posterior due to parameter uncertainty as a measure of epistemic…

When the cost of misclassifying a sample is high, it is useful to have an accurate estimate of uncertainty in the prediction for that sample. There are also multiple types of uncertainty which are best estimated in different ways, for…

Machine Learning · Computer Science 2019-03-18 Richard Harang , Ethan M. Rudd