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In recent years, Large Language Models (LLMs) have become fundamental to a broad spectrum of artificial intelligence applications. As the use of LLMs expands, precisely estimating the uncertainty in their predictions has become crucial.…

Artificial Intelligence · Computer Science 2024-10-29 Mohammad Beigi , Sijia Wang , Ying Shen , Zihao Lin , Adithya Kulkarni , Jianfeng He , Feng Chen , Ming Jin , Jin-Hee Cho , Dawei Zhou , Chang-Tien Lu , Lifu Huang

We present Fortuna, an open-source library for uncertainty quantification in deep learning. Fortuna supports a range of calibration techniques, such as conformal prediction that can be applied to any trained neural network to generate…

This paper surveys uncertainty-aware explainable artificial intelligence (UAXAI), examining how uncertainty is incorporated into explanatory pipelines and how such methods are evaluated. Across the literature, three recurring approaches to…

Artificial Intelligence · Computer Science 2026-03-31 Helena Löfström , Tuwe Löfström , Anders Hjort , Fatima Rabia Yapicioglu

This paper presents a data-driven framework for uncertainty propagation under unmeasured or statistically unmodeled (unstructured) disturbances. We consider residual disturbances, which consolidate all unstructured disturbances into a…

Systems and Control · Electrical Eng. & Systems 2026-05-18 Guanru Pan , Dirk Reinhardt , Sebastien Gros , Timm Faulwasser

With the widespread success of deep neural networks in science and technology, it is becoming increasingly important to quantify the uncertainty of the predictions produced by deep learning. In this paper, we introduce a new method that…

Machine Learning · Computer Science 2019-08-15 Qingyang Wu , He Li , Lexin Li , Zhou Yu

Deep neural networks (NNs) are powerful black box predictors that have recently achieved impressive performance on a wide spectrum of tasks. Quantifying predictive uncertainty in NNs is a challenging and yet unsolved problem. Bayesian NNs,…

Machine Learning · Statistics 2017-11-07 Balaji Lakshminarayanan , Alexander Pritzel , Charles Blundell

Given a universe of discourse X-a domain of possible outcomes-an experiment may consist of selecting one of its elements, subject to the operation of chance, or of observing the elements, subject to imprecision. A priori uncertainty about…

Artificial Intelligence · Computer Science 2013-03-26 Arthur Ramer

Bayesian clustering methods have the widely touted advantage of providing a probabilistic characterization of uncertainty in clustering through the posterior distribution. An amazing variety of priors and likelihoods have been proposed for…

Methodology · Statistics 2025-11-21 Garritt L. Page , Andrés F. Barrientos , David B. Dahl , David B. Dunson

High-quality estimates of uncertainty and robustness are crucial for numerous real-world applications, especially for deep learning which underlies many deployed ML systems. The ability to compare techniques for improving these estimates is…

This paper explores generalised probabilistic modelling and uncertainty estimation in comparative LLM-as-a-judge frameworks. We show that existing Product-of-Experts methods are specific cases of a broader framework, enabling diverse…

Artificial Intelligence · Computer Science 2025-05-22 Yassir Fathullah , Mark J. F. Gales

Reliable predictive uncertainty estimation plays an important role in enabling the deployment of neural networks to safety-critical settings. A popular approach for estimating the predictive uncertainty of neural networks is to define a…

Machine Learning · Statistics 2023-12-29 Tim G. J. Rudner , Zonghao Chen , Yee Whye Teh , Yarin Gal

Popular approaches for quantifying predictive uncertainty in deep neural networks often involve distributions over weights or multiple models, for instance via Markov Chain sampling, ensembling, or Monte Carlo dropout. These techniques…

Machine Learning · Computer Science 2023-03-08 Dennis Ulmer , Christian Hardmeier , Jes Frellsen

Uncertainty in machine learning is not generally taught as general knowledge in Machine Learning course curricula. In this paper we propose a short curriculum for a course about uncertainty in machine learning, and complement the course…

Machine Learning · Computer Science 2021-08-20 Matias Valdenegro-Toro

In many areas of engineering and sciences, decision rules and control strategies are usually designed based on nominal values of relevant system parameters. To ensure that a control strategy or decision rule will work properly when the…

Probability · Mathematics 2020-06-16 Xinjia Chen

This paper presents an approach for developing the explanation capabilities of rule-based expert systems managing imprecise and uncertain knowledge. The treatment of uncertainty takes place in the framework of possibility theory where the…

Artificial Intelligence · Computer Science 2013-04-08 Henri Farrency , Henri Prade

This paper studies the problem of distributed classification with a network of heterogeneous agents. The agents seek to jointly identify the underlying target class that best describes a sequence of observations. The problem is first…

Artificial Intelligence · Computer Science 2020-11-24 James Z. Hare , Cesar A. Uribe , Lance Kaplan , Ali Jadbabaie

The Shapley value provides a principled framework for fairly distributing rewards among participants according to their individual contributions. While prior work has applied this concept to data valuation in machine learning, existing…

Computer Science and Game Theory · Computer Science 2026-01-22 Zhuofan Jia , Jian Pei

Probability theory is far from being the most general mathematical theory of uncertainty. A number of arguments point at its inability to describe second-order ('Knightian') uncertainty. In response, a wide array of theories of uncertainty…

Statistics Theory · Mathematics 2021-04-15 Fabio Cuzzolin

Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using…

Machine Learning · Statistics 2019-05-28 Aliaksandr Hubin , Geir Storvik

Polynomial chaos based methods enable the efficient computation of output variability in the presence of input uncertainty in complex models. Consequently, they have been used extensively for propagating uncertainty through a wide variety…

Optimization and Control · Mathematics 2020-09-18 Tuhin Sahai