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In binary classification tasks, accurate representation of probabilistic predictions is essential for various real-world applications such as predicting payment defaults or assessing medical risks. The model must then be well-calibrated to…

Machine Learning · Computer Science 2024-08-08 Agathe Fernandes Machado , Arthur Charpentier , Emmanuel Flachaire , Ewen Gallic , François Hu

Measurement of uncertainty of predictions from machine learning methods is important across scientific domains and applications. We present, to our knowledge, the first such technique that quantifies the uncertainty of predictions from a…

Machine Learning · Statistics 2022-04-04 Alex Hagen , Karl Pazdernik , Nicole LaHaye , Marjolein Oostrom

Consider a multi-class labelling problem, where the labels can take values in $[k]$, and a predictor predicts a distribution over the labels. In this work, we study the following foundational question: Are there notions of multi-class…

Machine Learning · Computer Science 2024-06-11 Parikshit Gopalan , Lunjia Hu , Guy N. Rothblum

Delivering meaningful uncertainty estimates is essential for a successful deployment of machine learning models in the clinical practice. A central aspect of uncertainty quantification is the ability of a model to return predictions that…

Computer Vision and Pattern Recognition · Computer Science 2023-03-03 Adrian Galdran , Johan Verjans , Gustavo Carneiro , Miguel A. González Ballester

Methods for reasoning under uncertainty are a key building block of accurate and reliable machine learning systems. Bayesian methods provide a general framework to quantify uncertainty. However, because of model misspecification and the use…

Machine Learning · Computer Science 2018-07-03 Volodymyr Kuleshov , Nathan Fenner , Stefano Ermon

Accurate quantification of uncertainty is crucial for real-world applications of machine learning. However, modern deep neural networks still produce unreliable predictive uncertainty, often yielding over-confident predictions. In this…

Machine Learning · Computer Science 2020-10-29 Peng Cui , Wenbo Hu , Jun Zhu

A set of probabilistic predictions is well calibrated if the events that are predicted to occur with probability p do in fact occur about p fraction of the time. Well calibrated predictions are particularly important when machine learning…

Machine Learning · Statistics 2014-01-14 Mahdi Pakdaman Naeini , Gregory F. Cooper , Milos Hauskrecht

A key challenge in probabilistic regression is ensuring that predictive distributions accurately reflect true empirical uncertainty. Minimizing overall prediction error often encourages models to prioritize informativeness over calibration,…

Machine Learning · Statistics 2026-02-17 Ádám Jung , Domokos M. Kelen , András A. Benczúr

In this work, we propose a mean-squared error-based risk that enables the comparison and optimization of estimators of squared calibration errors in practical settings. Improving the calibration of classifiers is crucial for enhancing the…

Machine Learning · Computer Science 2025-02-24 Sebastian G. Gruber , Francis Bach

Optimal decision making requires that classifiers produce uncertainty estimates consistent with their empirical accuracy. However, deep neural networks are often under- or over-confident in their predictions. Consequently, methods have been…

In the recent literature on machine learning and decision making, calibration has emerged as a desirable and widely-studied statistical property of the outputs of binary prediction models. However, the algorithmic aspects of measuring model…

Machine Learning · Computer Science 2024-06-24 Lunjia Hu , Arun Jambulapati , Kevin Tian , Chutong Yang

Identification of model parameters in computer simulations is an important topic in computer experiments. We propose a new method, called the projected kernel calibration method, to estimate these model parameters. The proposed method is…

Methodology · Statistics 2017-05-10 Rui Tuo

Recent works have shown that most deep learning models are often poorly calibrated, i.e., they may produce overconfident predictions that are wrong. It is therefore desirable to have models that produce predictive uncertainty estimates that…

Machine Learning · Computer Science 2020-03-02 Saiteja Utpala , Piyush Rai

One prominent method of evaluating machine learning model trustworthiness is the notion of calibration. In the binary outcome setting, a probabilistic predictor is calibrated if outcomes are realized according to a model's distributional…

Machine Learning · Computer Science 2026-05-25 Jessica Finocchiaro , Victor Ganson , Drona Khurana

Confidence calibration of classification models is a technique to estimate the true posterior probability of the predicted class, which is critical for ensuring reliable decision-making in practical applications. Existing confidence…

Methodology · Statistics 2025-02-19 Jinzong Dong , Zhaohui Jiang , Dong Pan , Haoyang Yu

The task of calibration is to retrospectively adjust the outputs from a machine learning model to provide better probability estimates on the target variable. While calibration has been investigated thoroughly in classification, it has not…

Machine Learning · Statistics 2018-06-21 Hao Song , Meelis Kull , Peter Flach

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…

Probability predictions from binary regressions or machine learning methods ought to be calibrated: If an event is predicted to occur with probability $x$, it should materialize with approximately that frequency, which means that the…

Statistics Theory · Mathematics 2023-01-11 Timo Dimitriadis , Lutz Duembgen , Alexander Henzi , Marius Puke , Johanna Ziegel

Probabilistic classifiers output confidence scores along with their predictions, and these confidence scores should be calibrated, i.e., they should reflect the reliability of the prediction. Confidence scores that minimize standard metrics…

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