Measuring Uncertainty Calibration
Kamil Ciosek, Nicolò Felicioni, Sina Ghiassian, Juan Elenter, Francesco Tonolini, David Gustafsson, Eva Garcia-Martin, Carmen Barcena Gonzalez
Abstract
We make two contributions to the problem of estimating the $L_1$ calibration error of a binary classifier from a finite dataset. First, we provide an upper bound for any classifier where the calibration function has bounded variation. Second, we provide a method of modifying any classifier so that its calibration error can be upper bounded efficiently without significantly impacting classifier performance and without any restrictive assumptions. All our results are non-asymptotic and distribution-free. We conclude by providing advice on how to measure calibration error in practice. Our methods yield practical procedures that can be run on real-world datasets with modest overhead.
BibTeX
@inproceedings{
ciosek2026measuring,
title={Measuring Uncertainty Calibration},
author={Kamil Ciosek and Nicol{\`o} Felicioni and Sina Ghiassian and Juan Elenter and Francesco Tonolini and David Gustafsson and Eva Garcia-Martin and Carmen Barcena Gonzalez and Rapha{\"e}lle Bertrand-Lalo},
booktitle={The Fourteenth International Conference on Learning Representations},
year={2026},
url={https://openreview.net/forum?id=4AjfwNnWAV}
}