Machine learning applications require fast and reliable per-sample uncertainty estimation. A common approach is to use predictive distributions from Bayesian or approximation methods and additively decompose uncertainty into aleatoric (i.e., data-related) and epistemic (i.e., model-related) components. However, additive decomposition has recently been questioned, with evidence that it breaks down when using finite-ensemble sampling and/or mismatched predictive distributions. This paper introduces Variance-Gated Ensembles (VGE), an intuitive, differentiable framework that injects epistemic sensitivity via a signal-to-noise gate computed from ensemble statistics. VGE provides: (i) a Variance-Gated Margin Uncertainty (VGMU) score that couples decision margins with ensemble predictive variance; and (ii) a Variance-Gated Normalization (VGN) layer that generalizes the variance-gated uncertainty mechanism to training via per-class, learnable normalization of ensemble member probabilities. We derive closed-form vector-Jacobian products enabling end-to-end training through ensemble sample mean and variance. VGE matches or exceeds state-of-the-art information-theoretic baselines while remaining computationally efficient. As a result, VGE provides a practical and scalable approach to epistemic-aware uncertainty estimation in ensemble models.
Cooperative Variance Estimation and Bayesian Neural Networks for Disentangling Aleatoric and Epistemic Uncertainties
Faculty of Mechanical Engineering, Delft University of Technology, Mekelweg 2, Delft, 2628 CD, The Netherlands（代尔夫特理工大学机械工程学院）；School of Engineering, Brown University, 184 Hope St., Providence, RI 02912, USA（布朗大学工程学院）
Mila - Quebec AI Institute（米拉-魁北克人工智能研究所）；Université de Montréal（蒙特利尔大学）；Massachusetts Institute of Technology（麻省理工学院）
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 uncertainty, we argue that this does not capture the part of lack of knowledge induced by model misspecification. We discuss how the excess risk, which is the gap between the generalization error of a predictor and the Bayes predictor, is a sound measure of epistemic uncertainty which captures the effect of model misspecification. We thus propose a principl…
Technical University Munich（慕尼黑工业大学）；Autonomous Intelligent Driving GmbH（自主智能驾驶有限公司）；Google（谷歌）
We present a sampling-free approach for computing the epistemic uncertainty of a neural network. Epistemic uncertainty is an important quantity for the deployment of deep neural networks in safety-critical applications, since it represents how much one can trust predictions on new data. Recently promising works were proposed using noise injection combined with Monte-Carlo sampling at inference time to estimate this quantity (e.g. Monte-Carlo dropout). Our main contribution is an approximation of the epistemic uncertainty estimated by these methods that does not require sampling, thus notably r…
TRIAGE: Type-Routed Interventions via Aleatoric-Epistemic Gated Estimation in Robotic Manipulation and Adaptive Perception -- Don't Treat All Uncertainty the Same
University of Illinois at Chicago（伊利诺伊大学香槟分校）；Intel Labs（英特尔实验室）
Ensembles of neural networks (NNs) have long been used to estimate predictive uncertainty; a small number of NNs are trained from different initialisations and sometimes on differing versions of the dataset. The variance of the ensemble's predictions is interpreted as its epistemic uncertainty. The appeal of ensembling stems from being a collection of regular NNs - this makes them both scalable and easily implementable. They have achieved strong empirical results in recent years, often presented as a practical alternative to more costly Bayesian NNs (BNNs). The departure from Bayesian methodol…
A Posterior-Predictive Variance Decomposition for Epistemic and Aleatoric Uncertainty in Wind Power Forecasting
School of Engineering, Deakin University（德肯大学工程学院）；ARC Training Centre in Energy Technologies for Future Grids, School of Engineering, University of Wollongong（未来电网能源技术培训中心，沃林戈大学工程学院）
We propose a novel sparse spectrum approximation of Gaussian process (GP) tailored for Bayesian optimization. Whilst the current sparse spectrum methods provide desired approximations for regression problems, it is observed that this particular form of sparse approximations generates an overconfident GP, i.e. it produces less epistemic uncertainty than the original GP. Since the balance between predictive mean and the predictive variance is the key determinant to the success of Bayesian optimization, the current sparse spectrum methods are less suitable for it. We derive a new regularized marg…
Laplace-Fisher Gate Identities for Optimal Matrix-Gated Blended Score Estimation
The Oden Institute for Computational Engineering and Sciences（奥登计算工程与科学研究院）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）；The Department of Aerospace Engineering & Engineering Mechanics（航空航天工程与机械系）
Uncertainty Modeling in Graph Neural Networks via Stochastic Differential Equations
Department of Engineering, University of Cambridge（剑桥大学工程系）；Mathematical Institute, University of Oxford（牛津大学数学系）；Oxford-Man Institute of Quantitative Finance, University of Oxford（牛津大学量化金融研究所）；Department of Computer Science and Technology, University of Cambridge（剑桥大学计算机科学与技术系）
Model-Based Epistemic Variance of Values for Risk-Aware Policy Optimization
Bosch Corporate Research（博世公司研究中心）；Technical University Darmstadt（达姆施塔特工业大学）；German Research Center for Artificial Intelligence (DFKI)（德国人工智能研究中心）；Centre for Cognitive Science（认知科学中心）
Activation-Space Uncertainty Quantification for Pretrained Networks
Department of Engineering, University of Cambridge, Cambridge, UK（剑桥大学工程系）；Mathematical Institute（数学研究所）；Oxford-Man Institute, University of Oxford, Oxford, UK（牛津大学奥克斯曼研究所）
Osaka university（大阪大学）；The University of Tokyo（东京大学）
Bayesian deep learning plays an important role especially for its ability evaluating epistemic uncertainty (EU). Due to computational complexity issues, approximation methods such as variational inference (VI) have been used in practice to obtain posterior distributions and their generalization abilities have been analyzed extensively, for example, by PAC-Bayesian theory; however, little analysis exists on EU, although many numerical experiments have been conducted on it. In this study, we analyze the EU of supervised learning in approximate Bayesian inference by focusing on its excess risk. F…
College of Computer Science and Software Engineering, Shenzhen University（深圳大学计算机与软件工程学院）；The Guangdong Key Laboratory of Intelligent Information Processing, Shenzhen University（深圳大学广东省智能信息处理重点实验室）；College of Mathematics and Statistics, Shenzhen University（深圳大学数学与统计学院）；Department of Mathematics, The Chinese University of Hong Kong（香港中文大学数学系）
Quantifying the uncertainty of supervised learning models plays an important role in making more reliable predictions. Epistemic uncertainty, which usually is due to insufficient knowledge about the model, can be reduced by collecting more data or refining the learning models. Over the last few years, scholars have proposed many epistemic uncertainty handling techniques which can be roughly grouped into two categories, i.e., Bayesian and ensemble. This paper provides a comprehensive review of epistemic uncertainty learning techniques in supervised learning over the last five years. As such, we…
Efficient Epistemic Uncertainty Estimation for Large Language Models via Knowledge Distillation
Graduate School of Data Science, Seoul National University（首尔国立大学数据科学研究生院）；Department of Rural Systems Engineering, Seoul National University（首尔国立大学农村系统工程系）；Department of Aerospace Engineering, Seoul National University（首尔国立大学航空航天工程系）；Department of Electrical Engineering and Computer Science, Gwangju Institute of Science and Technology（全州科学科技研究院电子工程与计算机科学系）
An Axiomatic Assessment of Entropy- and Variance-based Uncertainty Quantification in Regression
LMU Munich（慕尼黑莱布尼茨大学）；Munich Center for Machine Learning (MCML)（慕尼黑机器学习中心）；DLR-German Aerospace Center University of Tromsø（德国航空航天中心图勒大学）；German Research Center for Artificial Intelligence (DFKI, DSA)（德国人工智能研究中心）
Surrogate Modelling of Proton Dose with Monte Carlo Dropout Uncertainty Quantification
Institute for Mathematical Innovation University of Bath, Bath, UK（数学创新研究所 英国巴斯大学）；Department of Mathematical Sciences University of Bath, Bath, UK（数学科学系 英国巴斯大学）
Multi-level Monte Carlo Dropout for Efficient Uncertainty Quantification
Institute for Mathematical Innovation University of Bath, Bath, UK（数学创新研究所 英国巴斯大学）；Department of Mathematical Sciences University of Bath, Bath, UK（数学科学系 英国巴斯大学）
Instituto de Ingenieria de Aragon (I3A)（阿拉贡工程研究所）；Universidad de Zaragoza（萨拉戈萨大学）
Affordances are a fundamental concept in robotics since they relate available actions for an agent depending on its sensory-motor capabilities and the environment. We present a novel Bayesian deep network to detect affordances in images, at the same time that we quantify the distribution of the aleatoric and epistemic variance at the spatial level. We adapt the Mask-RCNN architecture to learn a probabilistic representation using Monte Carlo dropout. Our results outperform the state-of-the-art of deterministic networks. We attribute this improvement to a better probabilistic feature space repre…
Korea University（高丽大学）；Electronics and Telecommunications Research Institute（电子与电信研究院）
Electronic health records (EHR) are characterized as non-stationary, heterogeneous, noisy, and sparse data; therefore, it is challenging to learn the regularities or patterns inherent within them. In particular, sparseness caused mostly by many missing values has attracted the attention of researchers, who have attempted to find a better use of all available samples for determining the solution of a primary target task through the defining a secondary imputation problem. Methodologically, existing methods, either deterministic or stochastic, have applied different assumptions to impute missing…
One step closer to unbiased aleatoric uncertainty estimation
Massachusetts Institute of Technology（麻省理工学院）；Harvard University（哈佛大学）；MIT-IBM Watson AI Lab（MIT-IBM沃森人工智能实验室）；IBM Research（IBM研究院）；University of California（加利福尼亚大学）
Argonne National Laboratory（阿贡国家实验室）；Université Paris-Saclay（巴黎萨克雷大学）
Deep neural networks are powerful predictors for a variety of tasks. However, they do not capture uncertainty directly. Using neural network ensembles to quantify uncertainty is competitive with approaches based on Bayesian neural networks while benefiting from better computational scalability. However, building ensembles of neural networks is a challenging task because, in addition to choosing the right neural architecture or hyperparameters for each member of the ensemble, there is an added cost of training each model. We propose AutoDEUQ, an automated approach for generating an ensemble of …
Imperial College London（伦敦帝国理工学院）；University of Kent（肯特大学）；University of Augsburg（奥格斯堡大学）
We focus on using the predictive uncertainty signal calculated by Bayesian neural networks to guide learning in the self-same task the model is being trained on. Not opting for costly Monte Carlo sampling of weights, we propagate the approximate hidden variance in an end-to-end manner, throughout a variational Bayesian adaptation of a ResNet with attention and squeeze-and-excitation blocks, in order to identify data samples that should contribute less into the loss value calculation. We, thus, propose uncertainty-aware, data-specific label smoothing, where the smoothing probability is dependen…
Instrumental and Proximal Causal Inference with Gaussian Processes
Department of Statistics and Actuarial Science, University of Hong Kong（香港大学统计与精算科学系）；Rational Intelligence Lab, CISPA Helmholtz Center for Information Security（CISPA霍普夫信息安全中心理性智能实验室）；Australian Institute for Machine Learning, Adelaide University（阿德莱德大学澳大利亚机器学习研究所）；College of Computing & Data Science, Nanyang Technological University（南洋理工大学计算与数据科学学院）
Epistemic uncertainty quantification is a crucial part of drawing credible conclusions from predictive models, whether concerned about the prediction at a given point or any downstream evaluation that uses the model as input. When the predictive model is simple and its evaluation differentiable, this task is solved by the delta method, where we propagate the asymptotically-normal uncertainty in the predictive model through the evaluation to compute standard errors and Wald confidence intervals. However, this becomes difficult when the model and/or evaluation becomes more complex. Remedies incl…
Variance-Reduced Manifold Sampling via Polynomial-Maximization Density Estimation
Department of Information, Multimedia Technologies and Design, Cherkasy State Business College（切爾卡西州商業學院信息、多媒體技術與設計系）；State Scientific Research Institute of Armament and Military Equipment Testing and Certification（武器和軍事設備測試和認證國家科學研究 institutes）；Department of Cybernetics and Applied Mathematics, Uzhhorod National University（烏茲霍羅德國家大學自動控制與應用數學系）
