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Inverse optimization (IO) is used to estimate unknown parameters of an optimization model from observed decisions. In the data-driven context, the estimated parameters are inherently uncertain, yet quantifying this uncertainty has received…

Optimization and Control · Mathematics 2026-05-26 Timothy C. Y. Chan , Nathan Sandholtz , Nasrin Yousefi

Bayesian model comparison (BMC) offers a principled probabilistic approach to study and rank competing models. In standard BMC, we construct a discrete probability distribution over the set of possible models, conditional on the observed…

Machine Learning · Statistics 2023-02-22 Marvin Schmitt , Stefan T. Radev , Paul-Christian Bürkner

The usual figure of merit characterizing the performance of neural networks applied to problems in the quantum domain is their accuracy, being the probability of a correct answer on a previously unseen input. Here we append this parameter…

Quantum Physics · Physics 2022-12-29 Jan Wasilewski , Tomasz Paterek , Karol Horodecki

Uncertainty quantification for image data is dominated by complex deep learning methods, yet the field lacks an interpretable, mathematically grounded baseline. We propose Bayesian scattering to fill this gap, serving as a first-step…

Machine Learning · Computer Science 2026-03-24 Bernardo Fichera , Zarko Ivkovic , Kjell Jorner , Philipp Hennig , Viacheslav Borovitskiy

Deep learning methods continue to have a decided impact on machine learning, both in theory and in practice. Statistical theoretical developments have been mostly concerned with approximability or rates of estimation when recovering…

Statistics Theory · Mathematics 2021-04-07 Yuexi Wang , Veronika Ročková

While neural networks have demonstrated impressive performance across various tasks, accurately quantifying uncertainty in their predictions is essential to ensure their trustworthiness and enable widespread adoption in critical systems.…

Machine Learning · Statistics 2025-11-11 Joseph Wilson , Chris van der Heide , Liam Hodgkinson , Fred Roosta

Uncertainty quantification in image retrieval is crucial for downstream decisions, yet it remains a challenging and largely unexplored problem. Current methods for estimating uncertainties are poorly calibrated, computationally expensive,…

Computer Vision and Pattern Recognition · Computer Science 2021-09-20 Frederik Warburg , Martin Jørgensen , Javier Civera , Søren Hauberg

Ensuring that predictions of machine learning (ML) classification models are accompanied by uncertainty estimates is one of the main pillars of trustworthy AI. Current research in uncertainty quantification focuses mainly on epistemic…

Machine Learning · Computer Science 2026-05-27 Samuel Bilson , Miles McCrory , Anna Pustogvar

Bayesian inference and uncertainty quantification in a general class of non-linear inverse regression models is considered. Analytic conditions on the regression model $\{\mathscr G(\theta): \theta \in \Theta\}$ and on Gaussian process…

Statistics Theory · Mathematics 2021-04-16 François Monard , Richard Nickl , Gabriel P. Paternain

This paper proposes a novel uncertainty quantification framework for computationally demanding systems characterized by a large vector of non-Gaussian uncertainties. It combines state-of-the-art techniques in advanced Monte Carlo sampling…

Computation · Statistics 2018-03-05 Phaedon-Stelios Koutsourelakis

Applications of large language models often involve the generation of free-form responses, in which case uncertainty quantification becomes challenging. This is due to the need to identify task-specific uncertainties (e.g., about the…

Computation and Language · Computer Science 2024-10-21 Ziyu Wang , Chris Holmes

Advances in architectural design, data availability, and compute have driven remarkable progress in semantic segmentation. Yet, these models often rely on relaxed Bayesian assumptions, omitting critical uncertainty information needed for…

Computer Vision and Pattern Recognition · Computer Science 2026-02-19 M. M. A. Valiuddin , R. J. G. van Sloun , C. G. A. Viviers , P. H. N. de With , F. van der Sommen

A reliable modeling of uncertain evidence in Bayesian networks based on a set-valued quantification is proposed. Both soft and virtual evidences are considered. We show that evidence propagation in this setup can be reduced to standard…

Artificial Intelligence · Computer Science 2018-02-16 Sabina Marchetti , Alessandro Antonucci

Explainable AI (XAI) aims to provide interpretations for predictions made by learning machines, such as deep neural networks, in order to make the machines more transparent for the user and furthermore trustworthy also for applications in…

Machine Learning · Computer Science 2020-06-17 Kirill Bykov , Marina M. -C. Höhne , Klaus-Robert Müller , Shinichi Nakajima , Marius Kloft

In chemistry, deep neural network models have been increasingly utilized in a variety of applications such as molecular property predictions, novel molecule designs, and planning chemical reactions. Despite the rapid increase in the use of…

Chemical Physics · Physics 2019-05-17 Seongok Ryu , Yongchan Kwon , Woo Youn Kim

Applying a machine learning model for decision-making in the real world requires to distinguish what the model knows from what it does not. A critical factor in assessing the knowledge of a model is to quantify its predictive uncertainty.…

Machine Learning · Computer Science 2023-11-15 Kajetan Schweighofer , Lukas Aichberger , Mykyta Ielanskyi , Sepp Hochreiter

Multi-fidelity models are becoming more prevalent in engineering, particularly in aerospace, as they combine both the computational efficiency of low-fidelity models with the high accuracy of higher-fidelity simulations. Various…

Computational Engineering, Finance, and Science · Computer Science 2024-07-09 Andrea Vaiuso , Gabriele Immordino , Marcello Righi , Andrea Da Ronch

The Best Estimate plus Uncertainty (BEPU) approach for nuclear systems modeling and simulation requires that the prediction uncertainty must be quantified in order to prove that the investigated design stays within acceptance criteria. A…

Computation · Statistics 2023-03-24 Ziyu Xie , Farah Alsafadi , Xu Wu

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

Unlike classification, whose goal is to estimate the class of each data point in a dataset, prevalence estimation or quantification is a task that aims to estimate the distribution of classes in a dataset. The two main tasks in prevalence…

Machine Learning · Statistics 2025-07-09 Aime Bienfait Igiraneza , Christophe Fraser , Robert Hinch