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The importance of accurately quantifying forecast uncertainty has motivated much recent research on probabilistic forecasting. In particular, a variety of deep learning approaches has been proposed, with forecast distributions obtained as…

Machine Learning · Statistics 2024-11-11 Benedikt Schulz , Lutz Köhler , Sebastian Lerch

In today's era, Neural Networks (NN) are applied in various scientific fields such as robotics, medicine, engineering, etc. However, the predictions of neural networks themselves contain a degree of uncertainty that must always be taken…

Machine Learning · Computer Science 2025-04-01 E. V. Aretos , D. G. Sotiropoulos

Machine learning models are often evaluated using point estimates of performance metrics such as accuracy, F1 score, or mean squared error. Such summaries fail to capture the inherent variability induced by stochastic elements of the…

Machine Learning · Computer Science 2026-05-13 Christoph Lehmann , Yahor Paromau

This paper presents a computationally feasible method to compute rigorous bounds on the interval-generalisation of regression analysis to account for epistemic uncertainty in the output variables. The new iterative method uses machine…

Data Analysis, Statistics and Probability · Physics 2023-02-22 Krasymyr Tretiak , Georg Schollmeyer , Scott Ferson

Effective decision making requires understanding the uncertainty inherent in a prediction. In regression, this uncertainty can be estimated by a variety of methods; however, many of these methods are laborious to tune, generate…

Machine Learning · Statistics 2021-12-02 Tianhui Zhou , Yitong Li , Yuan Wu , David Carlson

Neural networks are among the most powerful nonlinear models used to address supervised learning problems. Similar to most machine learning algorithms, neural networks produce point predictions and do not provide any prediction interval…

Machine Learning · Statistics 2020-07-01 Saeed Khaki , Dan Nettleton

Process Outcome Prediction entails predicting a discrete property of an unfinished process instance from its partial trace. High-capacity outcome predictors discovered with ensemble and deep learning methods have been shown to achieve top…

Machine Learning · Computer Science 2024-07-19 Francesco Folino , Luigi Pontieri , Pietro Sabatino

Understanding model performance on unlabeled data is a fundamental challenge of developing, deploying, and maintaining AI systems. Model performance is typically evaluated using test sets or periodic manual quality assessments, both of…

Machine Learning · Computer Science 2020-12-17 Benjamin Elder , Matthew Arnold , Anupama Murthi , Jiri Navratil

We study the well known difficult problem of prediction in measurement error models. By targeting directly at the prediction interval instead of the point prediction, we construct a prediction interval by providing estimators of both the…

Methodology · Statistics 2024-05-20 Fei Jiang , Yanyuan Ma

We study the generation of prediction intervals in regression for uncertainty quantification. This task can be formalized as an empirical constrained optimization problem that minimizes the average interval width while maintaining the…

Machine Learning · Statistics 2021-03-01 Haoxian Chen , Ziyi Huang , Henry Lam , Huajie Qian , Haofeng Zhang

As neural networks become more popular, the need for accompanying uncertainty estimates increases. There are currently two main approaches to test the quality of these estimates. Most methods output a density. They can be compared by…

Machine Learning · Statistics 2024-06-05 Laurens Sluijterman , Eric Cator , Tom Heskes

Recent work has shown that models trained to the same objective, and which achieve similar measures of accuracy on consistent test data, may nonetheless behave very differently on individual predictions. This inconsistency is undesirable in…

Machine Learning · Computer Science 2021-11-17 Emily Black , Klas Leino , Matt Fredrikson

Modern neural networks do not always produce well-calibrated predictions, even when trained with a proper scoring function such as cross-entropy. In classification settings, simple methods such as isotonic regression or temperature scaling…

Machine Learning · Computer Science 2021-03-26 Steven Reich , David Mueller , Nicholas Andrews

Future trajectories play an important role across domains such as autonomous driving, hurricane forecasting, and epidemic modeling, where practitioners commonly generate ensemble paths by sampling probabilistic models or leveraging multiple…

Machine Learning · Computer Science 2025-08-20 Ruipu Li , Daniel Menacho , Alexander Rodríguez

Ensemble weather forecasts enable a measure of uncertainty to be attached to each forecast, by computing the ensemble's spread. However, generating an ensemble with a good spread-error relationship is far from trivial, and a wide range of…

Atmospheric and Oceanic Physics · Physics 2021-01-05 Sebastian Scher , Gabriele Messori

A spatial point process can be characterized by an intensity function which predicts the number of events that occur across space. In this paper, we develop a method to infer predictive intensity intervals by learning a spatial model using…

Machine Learning · Statistics 2020-07-06 Muhammad Osama , Dave Zachariah , Petre Stoica

Ongoing developments in neural network models are continually advancing the state of the art in terms of system accuracy. However, the predicted labels should not be regarded as the only core output; also important is a well-calibrated…

Machine Learning · Statistics 2019-01-08 Gil Keren , Nicholas Cummins , Björn Schuller

Machine learning in asset pricing typically predicts expected returns as point estimates, ignoring uncertainty. We develop new methods to construct forecast confidence intervals for expected returns obtained from neural networks. We show…

Econometrics · Economics 2025-03-04 Yuan Liao , Xinjie Ma , Andreas Neuhierl , Linda Schilling

We propose a new optimization framework for aleatoric uncertainty estimation in regression problems. Existing methods can quantify the error in the target estimation, but they tend to underestimate it. To obtain the predictive uncertainty…

Computer Vision and Pattern Recognition · Computer Science 2021-03-12 Takumi Kawashima , Qing Yu , Akari Asai , Daiki Ikami , Kiyoharu Aizawa

Ensemble weather predictions require statistical post-processing of systematic errors to obtain reliable and accurate probabilistic forecasts. Traditionally, this is accomplished with distributional regression models in which the parameters…

Machine Learning · Statistics 2019-04-01 Stephan Rasp , Sebastian Lerch