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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…

This paper addresses uncertainty quantification (UQ) for problems where scalar (or low-dimensional vector) response quantities are insufficient and, instead, full-field (very high-dimensional) responses are of interest. To do so, an…

Probability · Mathematics 2018-04-18 D. G Giovanis , M. D. Shields

Machine learning (ML) offers promising new approaches to tackle complex problems and has been increasingly adopted in chemical and materials sciences. Broadly speaking, ML models employ generic mathematical functions and attempt to learn…

Materials Science · Physics 2024-08-21 Jin Dai , Santosh Adhikari , Mingjian Wen

Deep neural networks are prone to overconfident predictions on outliers. Bayesian neural networks and deep ensembles have both been shown to mitigate this problem to some extent. In this work, we aim to combine the benefits of the two…

Machine Learning · Computer Science 2021-11-08 Runa Eschenhagen , Erik Daxberger , Philipp Hennig , Agustinus Kristiadi

Uncertainty quantification (UQ) has become critical for evaluating the reliability of artificial intelligence systems, especially in medical image segmentation. This study addresses the interpretability of instance-wise uncertainty values…

Trustworthy depression prediction based on deep learning, incorporating both predictive reliability and algorithmic fairness across diverse demographic groups, is crucial for clinical application. Recently, achieving reliable depression…

Machine Learning · Computer Science 2025-10-01 Yonghong Li , Zheng Zhang , Xiuzhuang Zhou

Spatiotemporal prediction plays a critical role in numerous real-world applications such as urban planning, transportation optimization, disaster response, and pandemic control. In recent years, researchers have made significant progress by…

Machine Learning · Computer Science 2025-09-03 Dahai Yu , Dingyi Zhuang , Lin Jiang , Rongchao Xu , Xinyue Ye , Yuheng Bu , Shenhao Wang , Guang Wang

Applications, ranging from tracking molecular motion within cells to analyzing complex animal foraging behavior, require algorithms for associating a collection of spot-like particles in one image with particles contained in another image.…

Quantitative Methods · Quantitative Biology 2013-04-23 Alexander Mont , Aubrey V. Wiegel , Diego Krapf , Christopher P. Calderon

Deep learning has emerged as a promising paradigm to give access to highly accurate predictions of molecular and materials properties. A common short-coming shared by current approaches, however, is that neural networks only give point…

Computational Physics · Physics 2023-05-10 Albert Zhu , Simon Batzner , Albert Musaelian , Boris Kozinsky

Deep Ensembles, as a type of Bayesian Neural Networks, can be used to estimate uncertainty on the prediction of multiple neural networks by collecting votes from each network and computing the difference in those predictions. In this paper,…

Machine Learning · Computer Science 2023-07-10 Illia Oleksiienko , Alexandros Iosifidis

Predictions made by deep learning models are prone to data perturbations, adversarial attacks, and out-of-distribution inputs. To build a trusted AI system, it is therefore critical to accurately quantify the prediction uncertainties. While…

Machine Learning · Computer Science 2023-04-12 Hanjing Wang , Dhiraj Joshi , Shiqiang Wang , Qiang Ji

Inverse problems aim to determine model parameters of a mathematical problem from given observational data. Neural networks can provide an efficient tool to solve these problems. In the context of Bayesian inverse problems, Uncertainty…

Numerical Analysis · Mathematics 2025-09-16 Andrea Tonini , Tan Bui-Thanh , Francesco Regazzoni , Luca Dede' , Alfio Quarteroni

We present $\Delta$-UQ -- a novel, general-purpose uncertainty estimator using the concept of anchoring in predictive models. Anchoring works by first transforming the input into a tuple consisting of an anchor point drawn from a prior…

Machine Learning · Computer Science 2021-10-06 Rushil Anirudh , Jayaraman J. Thiagarajan

We provide single-model estimates of aleatoric and epistemic uncertainty for deep neural networks. To estimate aleatoric uncertainty, we propose Simultaneous Quantile Regression (SQR), a loss function to learn all the conditional quantiles…

Machine Learning · Statistics 2019-09-09 Natasa Tagasovska , David Lopez-Paz

Mixtures of multivariate normal inverse Gaussian (MNIG) distributions can be used to cluster data that exhibit features such as skewness and heavy tails. However, for cluster analysis, using a traditional finite mixture model framework,…

Methodology · Statistics 2020-05-13 Yuan Fang , Dimitris Karlis , Sanjeena Subedi

Machine learning methods are increasingly widely used in high-risk settings such as healthcare, transportation, and finance. In these settings, it is important that a model produces calibrated uncertainty to reflect its own confidence and…

Artificial Intelligence · Computer Science 2022-09-09 Sophia Sun

Measurement of uncertainty of predictions from machine learning methods is important across scientific domains and applications. We present, to our knowledge, the first such technique that quantifies the uncertainty of predictions from a…

Machine Learning · Statistics 2022-04-04 Alex Hagen , Karl Pazdernik , Nicole LaHaye , Marjolein Oostrom

There is a significant need for principled uncertainty reasoning in machine learning systems as they are increasingly deployed in safety-critical domains. A new approach with uncertainty-aware regression-based neural networks (NNs), based…

Machine Learning · Computer Science 2023-07-21 Nis Meinert , Jakob Gawlikowski , Alexander Lavin

Estimating parameters from data is a fundamental problem, customarily done by minimizing a loss function between a model and observed statistics. In scattering-based analysis, researchers often employ their domain expertise to select a…

Computational Physics · Physics 2024-09-05 Mengyang Gu , Yue He , Xubo Liu , Yimin Luo

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