Measuring Uncertainty Calibration

Kamil Ciosek; Nicolò Felicioni; Sina Ghiassian; Juan Elenter Litwin; Francesco Tonolini; David Gustafsson; Eva Garcia-Martin; Carmen Barcena Gonzalez; Raphaëlle Bertrand-Lalo

arXiv · 2512.13872

Measuring Uncertainty Calibration

Kamil Ciosek·Nicolò Felicioni·Sina Ghiassian·Juan Elenter Litwin·Francesco Tonolini·David Gustafsson·Eva Garcia-Martin·Carmen Barcena Gonzalez·Raphaëlle Bertrand-Lalo

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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.

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Kamil Ciosek, Nicolò Felicioni, Sina Ghiassian, Juan Elenter Litwin, Francesco Tonolini, David Gustafsson, Eva Garcia-Martin, Carmen Barcena Gonzalez, Raphaëlle Bertrand-Lalo. 2025-12-15. Measuring Uncertainty Calibration. https://arxiv.org/abs/2512.13872

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