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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…

Machine Learning · Computer Science 2026-02-10 H. Martin Gillis , Isaac Xu , Thomas Trappenberg

There are various measures of predictive uncertainty in the literature, but their relationships to each other remain unclear. This paper uses a decomposition of statistical pointwise risk into components, associated with different sources…

Machine Learning · Statistics 2025-02-18 Nikita Kotelevskii , Vladimir Kondratyev , Martin Takáč , Éric Moulines , Maxim Panov

Reliably estimating the uncertainty of a prediction throughout the model lifecycle is crucial in many safety-critical applications. The most common way to measure this uncertainty is via the predicted confidence. While this tends to work…

Machine Learning · Computer Science 2023-04-24 Sebastian G. Gruber , Florian Buettner

We present a Bayesian perspective on quantifying the uncertainty of graph signals estimated or reconstructed from imperfect observations. We show that many conventional methods of graph signal estimation, reconstruction and imputation, can…

Signal Processing · Electrical Eng. & Systems 2025-05-22 Lennard Rompelberg , Michael T. Schaub

Bayesian Neural Networks (BNNs) provide a tool to estimate the uncertainty of a neural network by considering a distribution over weights and sampling different models for each input. In this paper, we propose a method for uncertainty…

Machine Learning · Computer Science 2024-10-28 Illia Oleksiienko , Dat Thanh Tran , Alexandros Iosifidis

Quantifying predictive uncertainty of neural networks has recently attracted increasing attention. In this work, we focus on measuring uncertainty of graph neural networks (GNNs) for the task of node classification. Most existing GNNs model…

Machine Learning · Computer Science 2023-04-04 Zhao Xu , Carolin Lawrence , Ammar Shaker , Raman Siarheyeu

Effective quantification of uncertainty is an essential and still missing step towards a greater adoption of deep-learning approaches in different applications, including mission-critical ones. In particular, investigations on the…

Machine Learning · Computer Science 2023-04-14 Marco Forgione , Dario Piga

Uncertainty quantification is a critical aspect of machine learning models, providing important insights into the reliability of predictions and aiding the decision-making process in real-world applications. This paper proposes a novel way…

Machine Learning · Computer Science 2024-01-02 Yusuf Sale , Paul Hofman , Lisa Wimmer , Eyke Hüllermeier , Thomas Nagler

Real-world data contains aleatoric uncertainty - irreducible noise arising from imperfect measurements or from incomplete knowledge about the data generation process. Mean-variance estimation networks can learn this type of uncertainty but…

Machine Learning · Computer Science 2026-05-29 Jiaxiang Yi , Miguel A. Bessa

Uncertainty quantification is crucial for building reliable and trustable machine learning systems. We propose to estimate uncertainty in recurrent neural networks (RNNs) via stochastic discrete state transitions over recurrent timesteps.…

Machine Learning · Computer Science 2020-11-25 Cheng Wang , Carolin Lawrence , Mathias Niepert

Graph Neural Networks (GNN) provide a powerful framework that elegantly integrates Graph theory with Machine learning for modeling and analysis of networked data. We consider the problem of quantifying the uncertainty in predictions of GNN…

Machine Learning · Computer Science 2022-05-23 Sai Munikoti , Deepesh Agarwal , Laya Das , Balasubramaniam Natarajan

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

Uncertainty quantification for deep learning is a challenging open problem. Bayesian statistics offer a mathematically grounded framework to reason about uncertainties; however, approximate posteriors for modern neural networks still…

Machine Learning · Statistics 2020-01-23 Nicolas Brosse , Carlos Riquelme , Alice Martin , Sylvain Gelly , Éric Moulines

This paper proposes a fast and scalable method for uncertainty quantification of machine learning models' predictions. First, we show the principled way to measure the uncertainty of predictions for a classifier based on Nadaraya-Watson's…

The increasingly wide use of deep machine learning techniques in computational mechanics has significantly accelerated simulations of problems that were considered unapproachable just a few years ago. However, in critical applications such…

Machine Learning · Computer Science 2026-04-01 David Gonzalez , Alba Muixi , Beatriz Moya , Elias Cueto

We propose and investigate new complementary methodologies for estimating predictive variance networks in regression neural networks. We derive a locally aware mini-batching scheme that result in sparse robust gradients, and show how to…

Machine Learning · Statistics 2019-11-05 Nicki S. Detlefsen , Martin Jørgensen , Søren Hauberg

Image reconstruction methods based on deep neural networks have shown outstanding performance, equalling or exceeding the state-of-the-art results of conventional approaches, but often do not provide uncertainty information about the…

Computer Vision and Pattern Recognition · Computer Science 2020-12-01 Riccardo Barbano , Željko Kereta , Chen Zhang , Andreas Hauptmann , Simon Arridge , Bangti Jin

Neural networks are powerful tools in various applications, and quantifying their uncertainty is crucial for reliable decision-making. In the deep learning field, the uncertainties are usually categorized into aleatoric (data) and epistemic…

Machine Learning · Computer Science 2023-12-21 Wang Zhang , Ziwen Ma , Subhro Das , Tsui-Wei Weng , Alexandre Megretski , Luca Daniel , Lam M. Nguyen

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

Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the…

Numerical Analysis · Mathematics 2015-03-19 Kamaljit Chowdhary , Paul Dupuis
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