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Classifiers based on neural networks (NN) often lack a measure of uncertainty in the predicted class. We propose a method to estimate the probability mass function (PMF) of the different classes, as well as the covariance of the estimated…

Machine Learning · Computer Science 2024-10-28 Magnus Malmström , Isaac Skog , Daniel Axehill , Fredrik Gustafsson

Credal sets, i.e., closed convex sets of probability measures, provide a natural framework to represent aleatoric and epistemic uncertainty in machine learning. Yet how to quantify these two types of uncertainty for a given credal set,…

Reliable uncertainty from deterministic single-forward pass models is sought after because conventional methods of uncertainty quantification are computationally expensive. We take two complex single-forward-pass uncertainty approaches, DUQ…

Machine Learning · Computer Science 2022-01-31 Jishnu Mukhoti , Andreas Kirsch , Joost van Amersfoort , Philip H. S. Torr , Yarin Gal

Deep neural networks (DNNs) have been shown to perform well on exclusive, multi-class classification tasks. However, when different classes have similar visual features, it becomes challenging for human annotators to differentiate them.…

Computer Vision and Pattern Recognition · Computer Science 2024-04-18 Changbin Li , Kangshuo Li , Yuzhe Ou , Lance M. Kaplan , Audun Jøsang , Jin-Hee Cho , Dong Hyun Jeong , Feng Chen

We address the problem of uncertainty quantification and propose measures of total, aleatoric, and epistemic uncertainty based on a known decomposition of (strictly) proper scoring rules, a specific type of loss function, into a divergence…

Machine Learning · Computer Science 2025-05-29 Paul Hofman , Yusuf Sale , Eyke Hüllermeier

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

Epistemic uncertainty in neural networks is commonly modeled using two second-order paradigms: distribution-based representations, which rely on posterior parameter distributions, and set-based representations based on credal sets (convex…

Machine Learning · Computer Science 2026-02-27 Kaizheng Wang , Yunjia Wang , Fabio Cuzzolin , David Moens , Hans Hallez , Siu Lun Chau

The complexity of online decision-making under uncertainty stems from the requirement of finding a balance between exploiting known strategies and exploring new possibilities. Naturally, the uncertainty type plays a crucial role in…

Machine Learning · Computer Science 2025-03-07 Alireza Habibi , Saeed Ghoorchian , Setareh Maghsudi

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…

There are two major types of uncertainty one can model. Aleatoric uncertainty captures noise inherent in the observations. On the other hand, epistemic uncertainty accounts for uncertainty in the model -- uncertainty which can be explained…

Computer Vision and Pattern Recognition · Computer Science 2017-10-06 Alex Kendall , Yarin Gal

Deep neural networks are powerful tools to detect hidden patterns in data and leverage them to make predictions, but they are not designed to understand uncertainty and estimate reliable probabilities. In particular, they tend to be…

Machine Learning · Statistics 2022-11-10 Bat-Sheva Einbinder , Yaniv Romano , Matteo Sesia , Yanfei Zhou

Autonomous and semi-autonomous systems are using deep learning models to improve decision-making. However, deep classifiers can be overly confident in their incorrect predictions, a major issue especially in safety-critical domains. The…

Machine Learning · Computer Science 2024-12-05 Murat Sensoy , Lance M. Kaplan , Simon Julier , Maryam Saleki , Federico Cerutti

Efficient sampling from un-normalized target distributions is pivotal in scientific computing and machine learning. While neural samplers have demonstrated potential with a special emphasis on sampling efficiency, existing neural implicit…

Machine Learning · Computer Science 2024-11-05 Weijian Luo , Wei Deng

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

Predictive uncertainty-a model's self awareness regarding its accuracy on an input-is key for both building robust models via training interventions and for test-time applications such as selective classification. We propose a novel…

Machine Learning · Computer Science 2024-01-04 Nishant Jain , Karthikeyan Shanmugam , Pradeep Shenoy

Estimating and disentangling epistemic uncertainty, uncertainty that is reducible with more training data, and aleatoric uncertainty, uncertainty that is inherent to the task at hand, is critically important when applying machine learning…

Machine Learning · Computer Science 2024-11-08 Matthew A. Chan , Maria J. Molina , Christopher A. Metzler

Physics-informed neural networks (PINNs) have recently emerged as an alternative way of solving partial differential equations (PDEs) without the need of building elaborate grids, instead, using a straightforward implementation. In…

Analysis of PDEs · Mathematics 2019-09-04 Dongkun Zhang , Lu Lu , Ling Guo , George Em Karniadakis

For many applications it is critical to know the uncertainty of a neural network's predictions. While a variety of neural network parameter estimation methods have been proposed for uncertainty estimation, they have not been rigorously…

Machine Learning · Computer Science 2019-12-05 Nabeel Seedat , Christopher Kanan

Latent factor models are widely used to discover and adjust for hidden variation in modern applications. However, most methods do not fully account for uncertainty in the latent factors, which can lead to miscalibrated inferences such as…

Methodology · Statistics 2020-10-13 Jeffrey W. Miller , Scott L. Carter

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