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Modern neural networks tend to be overconfident on unseen, noisy or incorrectly labelled data and do not produce meaningful uncertainty measures. Bayesian deep learning aims to address this shortcoming with variational approximations (such…

Machine Learning · Statistics 2018-05-28 Nick Pawlowski , Andrew Brock , Matthew C. H. Lee , Martin Rajchl , Ben Glocker

Evidence-based deep learning represents a burgeoning paradigm for uncertainty estimation, offering reliable predictions with negligible extra computational overheads. Existing methods usually adopt Kullback-Leibler divergence to estimate…

Computer Vision and Pattern Recognition · Computer Science 2025-04-18 Yan Zhang , Ming Li , Chun Li , Zhaoxia Liu , Ye Zhang , Fei Richard Yu

Despite the functional success of deep neural networks (DNNs), their trustworthiness remains a crucial open challenge. To address this challenge, both testing and verification techniques have been proposed. But these existing techniques…

Machine Learning · Computer Science 2021-03-24 Teodora Baluta , Zheng Leong Chua , Kuldeep S. Meel , Prateek Saxena

Reliable uncertainty quantification is critical in high-stakes applications, such as medical diagnosis, where confidently incorrect predictions can erode trust in automated decision-making systems. Traditional uncertainty quantification…

Image and Video Processing · Electrical Eng. & Systems 2025-10-21 Hassan Gharoun , Mohammad Sadegh Khorshidi , Fang Chen , Amir H. Gandomi

Neural networks utilize the softmax as a building block in classification tasks, which contains an overconfidence problem and lacks an uncertainty representation ability. As a Bayesian alternative to the softmax, we consider a random…

Machine Learning · Computer Science 2020-06-30 Taejong Joo , Uijung Chung , Min-Gwan Seo

Confidence calibration is central to providing accurate and interpretable uncertainty estimates, especially under safety-critical scenarios. However, we find that existing calibration algorithms often overlook the issue of *proximity bias*,…

Machine Learning · Computer Science 2024-03-19 Miao Xiong , Ailin Deng , Pang Wei Koh , Jiaying Wu , Shen Li , Jianqing Xu , Bryan Hooi

It is known that neural networks have the problem of being over-confident when directly using the output label distribution to generate uncertainty measures. Existing methods mainly resolve this issue by retraining the entire model to…

Machine Learning · Computer Science 2022-12-15 Maohao Shen , Yuheng Bu , Prasanna Sattigeri , Soumya Ghosh , Subhro Das , Gregory Wornell

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

Deep neural networks can be roughly divided into deterministic neural networks and stochastic neural networks.The former is usually trained to achieve a mapping from input space to output space via maximum likelihood estimation for the…

Research has shown that deep networks tend to be overly optimistic about their predictions, leading to an underestimation of prediction errors. Due to the limited nature of data, existing studies have proposed various methods based on model…

Machine Learning · Computer Science 2023-10-24 Jia-Qi Yang , De-Chuan Zhan , Le Gan

Neural Networks have high accuracy in solving problems where it is difficult to detect patterns or create a logical model. However, these algorithms sometimes return wrong solutions, which become problematic in high-risk domains like…

Machine Learning · Computer Science 2025-06-26 Miguel N. Font , José L. Jorro-Aragoneses , Carlos M. Alaíz

Quantification is a supervised learning task that consists in predicting, given a set of classes C and a set D of unlabelled items, the prevalence (or relative frequency) p(c|D) of each class c in C. Quantification can in principle be…

Machine Learning · Computer Science 2021-09-22 Andrea Esuli , Alejandro Moreo Fernández , Fabrizio Sebastiani

Quantifying uncertainty is important for actionable predictions in real-world applications. A crucial part of predictive uncertainty quantification is the estimation of epistemic uncertainty, which is defined as an integral of the product…

Machine Learning · Computer Science 2023-10-25 Kajetan Schweighofer , Lukas Aichberger , Mykyta Ielanskyi , Günter Klambauer , Sepp Hochreiter

We study the problem of actively learning a classifier with a low calibration error. One of the most popular Acquisition Functions (AFs) in pool-based Active Learning (AL) is querying by the model's uncertainty. However, we recognize that…

Machine Learning · Computer Science 2025-10-06 Ha Manh Bui , Iliana Maifeld-Carucci , Anqi Liu

Some applications of deep learning require not only to provide accurate results but also to quantify the amount of confidence in their prediction. The management of an electric power grid is one of these cases: to avoid risky scenarios,…

Machine Learning · Computer Science 2023-08-25 Michele Guerra , Simone Scardapane , Filippo Maria Bianchi

In many classification problems it is desirable to output well-calibrated probabilities on the different classes. We propose a robust, non-parametric method of calibrating probabilities called SplineCalib that utilizes smoothing splines to…

Machine Learning · Statistics 2018-09-21 Brian Lucena

Mixup~\cite{zhang2017mixup} is a recently proposed method for training deep neural networks where additional samples are generated during training by convexly combining random pairs of images and their associated labels. While simple to…

Machine Learning · Statistics 2020-01-08 Sunil Thulasidasan , Gopinath Chennupati , Jeff Bilmes , Tanmoy Bhattacharya , Sarah Michalak

In safety-critical applications, language models should be able to characterize their uncertainty with meaningful probabilities. Many uncertainty quantification approaches require supervised data; however, finding suitable unseen…

Computation and Language · Computer Science 2026-05-14 Sophia Hager , Simon Zeng , Nicholas Andrews

Uncertainty Quantification (UQ) is essential in probabilistic machine learning models, particularly for assessing the reliability of predictions. In this paper, we present a systematic framework for estimating both epistemic and aleatoric…

Machine Learning · Statistics 2025-09-11 Marzieh Ajirak , Anand Ravishankar , Petar M. Djuric

Reliable uncertainty estimation is critical for deploying neural networks (NNs) in real-world applications. While existing calibration techniques often rely on post-hoc adjustments or coarse-grained binning methods, they remain limited in…

Machine Learning · Computer Science 2025-05-30 Pedro Mendes , Paolo Romano , David Garlan