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We study loss functions that measure the accuracy of a prediction based on multiple data points simultaneously. To our knowledge, such loss functions have not been studied before in the area of property elicitation or in machine learning…

Machine Learning · Computer Science 2017-06-06 Sebastian Casalaina-Martin , Rafael Frongillo , Tom Morgan , Bo Waggoner

Optimizing proper loss functions is popularly believed to yield predictors with good calibration properties; the intuition being that for such losses, the global optimum is to predict the ground-truth probabilities, which is indeed…

Machine Learning · Computer Science 2023-12-11 Jarosław Błasiok , Parikshit Gopalan , Lunjia Hu , Preetum Nakkiran

ML models have errors when used for predictions. The errors are unknown but can be quantified by model uncertainty. When multiple ML models are trained using the same training points, their model uncertainties may be statistically…

Machine Learning · Statistics 2025-09-23 Xiaoping Du

The accuracy of machine learning systems is a widely studied research topic. Established techniques such as cross-validation predict the accuracy on unseen data of the classifier produced by applying a given learning method to a given…

Machine Learning · Computer Science 2012-12-06 J. E. Smith , P. Caleb-Solly , M. A. Tahir , D. Sannen , H. van-Brussel

With rapid adoption of deep learning in critical applications, the question of when and how much to trust these models often arises, which drives the need to quantify the inherent uncertainties. While identifying all sources that account…

Machine Learning · Statistics 2019-11-22 Jayaraman J. Thiagarajan , Bindya Venkatesh , Prasanna Sattigeri , Peer-Timo Bremer

Many tasks in natural language processing can be viewed as multi-label classification problems. However, most of the existing models are trained with the standard cross-entropy loss function and use a fixed prediction policy (e.g., a…

Computation and Language · Computer Science 2019-09-11 Jiawei Wu , Wenhan Xiong , William Yang Wang

We propose and analyze a novel theoretical and algorithmic framework for structured prediction. While so far the term has referred to discrete output spaces, here we consider more general settings, such as manifolds or spaces of probability…

Machine Learning · Statistics 2020-02-14 Carlo Ciliberto , Lorenzo Rosasco , Alessandro Rudi

We introduce a new protocol for prediction with expert advice in which each expert evaluates the learner's and his own performance using a loss function that may change over time and may be different from the loss functions used by the…

Machine Learning · Computer Science 2009-03-23 Alexey Chernov , Vladimir Vovk

Accurate probabilistic predictions can be characterized by two properties -- calibration and sharpness. However, standard maximum likelihood training yields models that are poorly calibrated and thus inaccurate -- a 90% confidence interval…

Machine Learning · Computer Science 2025-05-14 Volodymyr Kuleshov , Shachi Deshpande

This paper tackles the challenge of detecting unreliable behavior in regression algorithms, which may arise from intrinsic variability (e.g., aleatoric uncertainty) or modeling errors (e.g., model uncertainty). First, we formally introduce…

Machine Learning · Computer Science 2024-06-12 Andres Altieri , Marco Romanelli , Georg Pichler , Florence Alberge , Pablo Piantanida

Calibration is a critical property for establishing the trustworthiness of predictors that provide uncertainty estimates. Multicalibration is a strengthening of calibration which requires that predictors be calibrated on a potentially…

Machine Learning · Computer Science 2025-09-23 Nathan Derhake , Siddartha Devic , Dutch Hansen , Kuan Liu , Vatsal Sharan

This book chapter introduces the principles and practical applications of uncertainty quantification in machine learning. It explains how to identify and distinguish between different types of uncertainty and presents methods for…

Machine Learning · Computer Science 2025-10-08 Hans Weytjens , Wouter Verbeke

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

We study calibration in question answering, estimating whether model correctly predicts answer for each question. Unlike prior work which mainly rely on the model's confidence score, our calibrator incorporates information about the input…

Computation and Language · Computer Science 2021-06-04 Shujian Zhang , Chengyue Gong , Eunsol Choi

We address the problem of uncertainty quantification and propose measures of total, aleatoric, and epistemic uncertainty based on a known decomposition of (strictly) proper scoring rules, a specific type of loss function, into a divergence…

Machine Learning · Computer Science 2025-05-29 Paul Hofman , Yusuf Sale , Eyke Hüllermeier

Neural networks solving real-world problems are often required not only to make accurate predictions but also to provide a confidence level in the forecast. The calibration of a model indicates how close the estimated confidence is to the…

Neural and Evolutionary Computing · Computer Science 2023-03-21 Ruslan Vasilev , Alexander D'yakonov

In order to identify expertise, forecasters should not be tested by their calibration score, which can always be made arbitrarily small, but rather by their Brier score. The Brier score is the sum of the calibration score and the refinement…

Theoretical Economics · Economics 2026-03-20 Dean P. Foster , Sergiu Hart

Classifier calibration has received recent attention from the machine learning community due both to its practical utility in facilitating decision making, as well as the observation that modern neural network classifiers are poorly…

Machine Learning · Computer Science 2022-05-24 John Kirchenbauer , Jacob Oaks , Eric Heim

Reliable uncertainty estimates are an important tool for helping autonomous agents or human decision makers understand and leverage predictive models. However, existing approaches to estimating uncertainty largely ignore the possibility of…

Machine Learning · Computer Science 2020-05-22 Sangdon Park , Osbert Bastani , James Weimer , Insup Lee

Modern neural networks are very powerful predictive models, but they are often incapable of recognizing when their predictions may be wrong. Closely related to this is the task of out-of-distribution detection, where a network must…

Machine Learning · Statistics 2018-02-15 Terrance DeVries , Graham W. Taylor
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