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Computational models support high-stakes decisions across engineering and science, and practitioners increasingly seek probabilistic predictions to quantify uncertainty in such models. Existing approaches generate predictions either by…

Computational Engineering, Finance, and Science · Computer Science 2026-04-13 Rileigh Bandy , Enrico Camporeale , Andong Hu , Thomas Berger , Rebecca Morrison

Bayesian neural networks with latent variables are scalable and flexible probabilistic models: They account for uncertainty in the estimation of the network weights and, by making use of latent variables, can capture complex noise patterns…

Machine Learning · Statistics 2018-06-19 Stefan Depeweg , José Miguel Hernández-Lobato , Finale Doshi-Velez , Steffen Udluft

When the cost of misclassifying a sample is high, it is useful to have an accurate estimate of uncertainty in the prediction for that sample. There are also multiple types of uncertainty which are best estimated in different ways, for…

Machine Learning · Computer Science 2019-03-18 Richard Harang , Ethan M. Rudd

Machine learning models have undeniably achieved impressive performance across a range of applications. However, their often perceived black-box nature, and lack of transparency in decision-making, have raised concerns about understanding…

Machine Learning · Computer Science 2023-10-03 Sein Minn

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

Model correction is essential for reliable PDE learning when the governing physics is misspecified due to simplified assumptions or limited observations. In the machine learning literature, existing correction methods typically operate in…

Numerical Analysis · Mathematics 2026-03-27 Wenwen Zhou , Xiaodong Feng , Ling Guo , Hao Wu

With the rise of the popularity and usage of neural networks, trustworthy uncertainty estimation is becoming increasingly essential. One of the most prominent uncertainty estimation methods is Deep Ensembles (Lakshminarayanan et al., 2017)…

Machine Learning · Statistics 2023-08-04 Laurens Sluijterman , Eric Cator , Tom Heskes

Reliable probability estimation is of crucial importance in many real-world applications where there is inherent (aleatoric) uncertainty. Probability-estimation models are trained on observed outcomes (e.g. whether it has rained or not, or…

The topic of deep learning has seen a surge of interest in recent years both within and outside of the field of Statistics. Deep models leverage both nonlinearity and interaction effects to provide superior predictions in many cases when…

Methodology · Statistics 2020-09-18 Paul A. Parker , Scott H. Holan

Accurately estimating the informativeness of individual samples in a dataset is an important objective in deep learning, as it can guide sample selection, which can improve model efficiency and accuracy by removing redundant or potentially…

Machine Learning · Computer Science 2025-05-22 Johannes Kaiser , Kristian Schwethelm , Daniel Rueckert , Georgios Kaissis

Equivariant models leverage prior knowledge on symmetries to improve predictive performance, but misspecified architectural constraints can harm it instead. While work has explored learning or relaxing constraints, selecting among…

Machine Learning · Computer Science 2025-07-16 Putri A. van der Linden , Alexander Timans , Dharmesh Tailor , Erik J. Bekkers

With model trustworthiness being crucial for sensitive real-world applications, practitioners are putting more and more focus on improving the uncertainty calibration of deep neural networks. Calibration errors are designed to quantify the…

Machine Learning · Computer Science 2024-03-14 Sebastian G. Gruber , Florian Buettner

Neural Linear Models (NLM) are deep Bayesian models that produce predictive uncertainties by learning features from the data and then performing Bayesian linear regression over these features. Despite their popularity, few works have…

Machine Learning · Statistics 2021-12-17 Sujay Thakur , Cooper Lorsung , Yaniv Yacoby , Finale Doshi-Velez , Weiwei Pan

We consider the problem of uncertainty estimation in the context of (non-Bayesian) deep neural classification. In this context, all known methods are based on extracting uncertainty signals from a trained network optimized to solve the…

Machine Learning · Computer Science 2019-04-25 Yonatan Geifman , Guy Uziel , Ran El-Yaniv

Uncertainty quantification in automated image analysis is highly desired in many applications. Typically, machine learning models in classification or segmentation are only developed to provide binary answers; however, quantifying the…

We present a deep transformation model for probabilistic regression. Deep learning is known for outstandingly accurate predictions on complex data but in regression tasks, it is predominantly used to just predict a single number. This…

Machine Learning · Statistics 2020-04-02 Beate Sick , Torsten Hothorn , Oliver Dürr

Comparing competing mathematical models of complex natural processes is a shared goal among many branches of science. The Bayesian probabilistic framework offers a principled way to perform model comparison and extract useful metrics for…

Quantifying the uncertainty of supervised learning models plays an important role in making more reliable predictions. Epistemic uncertainty, which usually is due to insufficient knowledge about the model, can be reduced by collecting more…

Machine Learning · Computer Science 2022-01-27 Xinlei Zhou , Han Liu , Farhad Pourpanah , Tieyong Zeng , Xizhao Wang

We develop variational Laplace for Bayesian neural networks (BNNs) which exploits a local approximation of the curvature of the likelihood to estimate the ELBO without the need for stochastic sampling of the neural-network weights. The…

Machine Learning · Statistics 2021-07-21 Ali Unlu , Laurence Aitchison

We develop variational Laplace for Bayesian neural networks (BNNs) which exploits a local approximation of the curvature of the likelihood to estimate the ELBO without the need for stochastic sampling of the neural-network weights. The…

Machine Learning · Statistics 2021-08-11 Ali Unlu , Laurence Aitchison