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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

Deep neural networks(NNs) have achieved impressive performance, often exceed human performance on many computer vision tasks. However, one of the most challenging issues that still remains is that NNs are overconfident in their predictions,…

Machine Learning · Computer Science 2019-12-30 Chanwoo Park , Jae Myung Kim , Seok Hyeon Ha , Jungwoo Lee

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

Bayesian neural networks (BNNs) with latent variables are probabilistic models which can automatically identify complex stochastic patterns in the data. We describe and study in these models a decomposition of predictive uncertainty into…

Machine Learning · Statistics 2017-11-15 Stefan Depeweg , José Miguel Hernández-Lobato , Finale Doshi-Velez , Steffen Udluft

Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using…

Machine Learning · Statistics 2019-05-28 Aliaksandr Hubin , Geir Storvik

We derive a novel sensitivity analysis of input variables for predictive epistemic and aleatoric uncertainty. We use Bayesian neural networks with latent variables as a model class and illustrate the usefulness of our sensitivity analysis…

Machine Learning · Statistics 2017-12-12 Stefan Depeweg , José Miguel Hernández-Lobato , Steffen Udluft , Thomas Runkler

Uncertainty quantification is a central challenge in reliable and trustworthy machine learning. Naive measures such as last-layer scores are well-known to yield overconfident estimates in the context of overparametrized neural networks.…

Machine Learning · Computer Science 2023-05-24 Lucas Clarté , Bruno Loureiro , Florent Krzakala , Lenka Zdeborová

In Hezaveh et al. 2017 we showed that deep learning can be used for model parameter estimation and trained convolutional neural networks to determine the parameters of strong gravitational lensing systems. Here we demonstrate a method for…

Cosmology and Nongalactic Astrophysics · Physics 2017-11-29 Laurence Perreault Levasseur , Yashar D. Hezaveh , Risa H. Wechsler

Quantifying model uncertainty is critical for understanding prediction reliability, yet distinguishing between aleatoric and epistemic uncertainty remains challenging. We extend recent work from classification to regression to provide a…

Inputs to machine learning models can have associated noise or uncertainties, but they are often ignored and not modelled. It is unknown if Bayesian Neural Networks and their approximations are able to consider uncertainty in their inputs.…

Machine Learning · Computer Science 2025-01-15 Matias Valdenegro-Toro , Marco Zullich

Deep neural networks have achieved impressive results on a wide variety of tasks. However, quantifying uncertainty in the network's output is a challenging task. Bayesian models offer a mathematical framework to reason about model…

Machine Learning · Computer Science 2019-05-28 Manikanta Srikar Yellapragada , Chandra Prakash Konkimalla

We combine Bayesian prediction and weighted inference as a unified approach to survey inference. The general principles of Bayesian analysis imply that models for survey outcomes should be conditional on all variables that affect the…

Methodology · Statistics 2020-06-24 Yajuan Si , Rob Trangucci , Jonah Sol Gabry , Andrew Gelman

Rigorous statistical methods, including parameter estimation with accompanying uncertainties, underpin the validity of scientific discovery, especially in the natural sciences. With increasingly complex data models such as deep learning…

Machine Learning · Computer Science 2026-02-18 Aurora Grefsrud , Nello Blaser , Trygve Buanes

Neural networks are popular state-of-the-art models for many different tasks.They are often trained via back-propagation to find a value of the weights that correctly predicts the observed data. Although back-propagation has shown good…

Machine Learning · Statistics 2020-12-29 Simón Rodríguez Santana , Daniel Hernández-Lobato

Uncertainty quantification in deep learning is crucial for safe and reliable decision-making in downstream tasks. Existing methods quantify uncertainty at the last layer or other approximations of the network which may miss some sources of…

Machine Learning · Statistics 2025-04-25 James McInerney , Nathan Kallus

As modern neural networks get more complex, specifying a model with high predictive performance and sound uncertainty quantification becomes a more challenging task. Despite some promising theoretical results on the true posterior…

Machine Learning · Computer Science 2025-06-18 Alisa Sheinkman , Sara Wade

Bayesian Neural Networks with Latent Variables (BNN+LVs) capture predictive uncertainty by explicitly modeling model uncertainty (via priors on network weights) and environmental stochasticity (via a latent input noise variable). In this…

Machine Learning · Computer Science 2022-09-19 Yaniv Yacoby , Weiwei Pan , Finale Doshi-Velez

Deep neural networks offer numerous potential applications across geoscience, for example, one could argue that they are the state-of-the-art method for predicting faults in seismic datasets. In quantitative reservoir characterization…

Machine Learning · Computer Science 2021-05-26 Lukas Mosser , Ehsan Zabihi Naeini

We establish estimations for the parameters of the output distribution for the softmax activation function using the probit function. As an application, we develop a new efficient Bayesian learning algorithm for fully connected neural…

Machine Learning · Computer Science 2023-02-01 Tianbo Yang , Tianshuo Yang

We consider inference from non-random samples in data-rich settings where high-dimensional auxiliary information is available both in the sample and the target population, with survey inference being a special case. We propose a regularized…

Methodology · Statistics 2021-04-13 Yutao Liu , Andrew Gelman , Qixuan Chen