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A simple method for adding uncertainty to neural network regression tasks via estimation of a general probability distribution is described. The methodology supports estimation of heteroscedastic, asymmetric uncertainties by a simple…

Atmospheric and Oceanic Physics · Physics 2021-09-16 Elizabeth A. Barnes , Randal J. Barnes , Nicolas Gordillo

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

Flow-based generative models parameterize probability distributions through an invertible transformation and can be trained by maximum likelihood. Invertible residual networks provide a flexible family of transformations where only…

Machine Learning · Statistics 2020-07-27 Ricky T. Q. Chen , Jens Behrmann , David Duvenaud , Jörn-Henrik Jacobsen

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

Quantifying uncertainty in a model's predictions is important as it enables the safety of an AI system to be increased by acting on the model's output in an informed manner. This is crucial for applications where the cost of an error is…

Computer Vision and Pattern Recognition · Computer Science 2021-05-31 Aria Khoshsirat

Modern machine learning methods including deep learning have achieved great success in predictive accuracy for supervised learning tasks, but may still fall short in giving useful estimates of their predictive {\em uncertainty}. Quantifying…

Modern neural networks have found to be miscalibrated in terms of confidence calibration, i.e., their predicted confidence scores do not reflect the observed accuracy or precision. Recent work has introduced methods for post-hoc confidence…

Computer Vision and Pattern Recognition · Computer Science 2021-09-22 Fabian Küppers , Jan Kronenberger , Jonas Schneider , Anselm Haselhoff

A Bayesian treatment of deep learning allows for the computation of uncertainties associated with the predictions of deep neural networks. We show how the concept of Errors-in-Variables can be used in Bayesian deep regression to also…

Machine Learning · Computer Science 2023-05-15 Jörg Martin , Clemens Elster

It is tempting to think that machines are less prone to unfairness and prejudice. However, machine learning approaches compute their outputs based on data. While biases can enter at any stage of the development pipeline, models are…

Computer Vision and Pattern Recognition · Computer Science 2020-12-07 Patrick Esser , Robin Rombach , Björn Ommer

Uncertainty quantification is an important and challenging problem in deep learning. Previous methods rely on dropout layers which are not present in modern deep architectures or batch normalization which is sensitive to batch sizes. In…

Computer Vision and Pattern Recognition · Computer Science 2020-07-10 Lukasz Wandzik , Raul Vicente Garcia , Jörg Krüger

Can regularization terms in the training of invertible neural networks lead to known Bayesian point estimators in reconstruction? Invertible networks are attractive for inverse problems due to their inherent stability and interpretability.…

Machine Learning · Computer Science 2025-10-31 Nick Heilenkötter

Uncertainty quantification is essential when deploying learning-based control methods in safety-critical systems. This is commonly realized by constructing uncertainty tubes that enclose the unknown function of interest, e.g., the reward…

Systems and Control · Electrical Eng. & Systems 2026-04-02 Abdullah Tokmak , Toni Karvonen , Thomas B. Schön , Dominik Baumann

Learning-based methods for inverse problems, adapting to the data's inherent structure, have become ubiquitous in the last decade. Besides empirical investigations of their often remarkable performance, an increasing number of works…

Numerical Analysis · Mathematics 2023-07-21 Clemens Arndt , Sören Dittmer , Nick Heilenkötter , Meira Iske , Tobias Kluth , Judith Nickel

Neural networks are vulnerable to input perturbations such as additive noise and adversarial attacks. In contrast, human perception is much more robust to such perturbations. The Bayesian brain hypothesis states that human brains use an…

Machine Learning · Computer Science 2020-11-11 Yujia Huang , James Gornet , Sihui Dai , Zhiding Yu , Tan Nguyen , Doris Y. Tsao , Anima Anandkumar

Bringing deep neural networks (DNNs) into safety critical applications such as automated driving, medical imaging and finance, requires a thorough treatment of the model's uncertainties. Training deep neural networks is already resource…

Computer Vision and Pattern Recognition · Computer Science 2022-05-31 Julian Burghoff , Robin Chan , Hanno Gottschalk , Annika Muetze , Tobias Riedlinger , Matthias Rottmann , Marius Schubert

Neural networks have proven successful at learning from complex data distributions by acting as universal function approximators. However, they are often overconfident in their predictions, which leads to inaccurate and miscalibrated…

Machine Learning · Computer Science 2021-02-23 Jeffrey Willette , Juho Lee , Sung Ju Hwang

Explainability and uncertainty quantification are key to trustable artificial intelligence. However, the reasoning behind uncertainty estimates is generally left unexplained. Identifying the drivers of uncertainty complements explanations…

Machine Learning · Computer Science 2025-05-13 Pascal Iversen , Simon Witzke , Katharina Baum , Bernhard Y. Renard

Training deep feature hierarchies to solve supervised learning tasks has achieved state of the art performance on many problems in computer vision. However, a principled way in which to train such hierarchies in the unsupervised setting has…

Computer Vision and Pattern Recognition · Computer Science 2015-09-11 Ross Goroshin , Michael Mathieu , Yann LeCun

While deep neural networks are highly performant and successful in a wide range of real-world problems, estimating their predictive uncertainty remains a challenging task. To address this challenge, we propose and implement a loss function…

Machine Learning · Computer Science 2022-10-14 Tony Tohme , Kevin Vanslette , Kamal Youcef-Toumi

A Bayesian net (BN) is more than a succinct way to encode a probabilistic distribution; it also corresponds to a function used to answer queries. A BN can therefore be evaluated by the accuracy of the answers it returns. Many algorithms for…

Artificial Intelligence · Computer Science 2013-02-08 Russell Greiner , Adam J. Grove , Dale Schuurmans
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