Verified Uncertainty Calibration

TLDR

Applications such as weather forecasting and personalized medicine demand models that output calibrated probability estimates, yet most models are not calibrated out of the box and require post‑processing. The authors introduce the scaling‑binning calibrator, combining parametric scaling and histogram binning to achieve calibrated predictions. The scaling‑binning calibrator first applies temperature‑like scaling to reduce variance, then bins the scaled outputs; this hybrid approach requires only O(1/ε² + B) samples, improving over histogram binning’s O(B/ε²) requirement. The study shows that existing recalibration methods are less calibrated than claimed and cannot quantify miscalibration, while the scaling‑binning calibrator achieves lower calibration error—35 % better than histogram binning on CIFAR‑10 and ImageNet—and offers provable calibration guarantees.

Abstract

Applications such as weather forecasting and personalized medicine demand models that output calibrated probability estimates---those representative of the true likelihood of a prediction. Most models are not calibrated out of the box but are recalibrated by post-processing model outputs. We find in this work that popular recalibration methods like Platt scaling and temperature scaling are (i) less calibrated than reported, and (ii) current techniques cannot estimate how miscalibrated they are. An alternative method, histogram binning, has measurable calibration error but is sample inefficient---it requires $O(B/\epsilon^2)$ samples, compared to $O(1/\epsilon^2)$ for scaling methods, where $B$ is the number of distinct probabilities the model can output. To get the best of both worlds, we introduce the scaling-binning calibrator, which first fits a parametric function that acts like a baseline for variance reduction and then bins the function values to actually ensure calibration. This requires only $O(1/\epsilon^2 + B)$ samples. We then show that methods used to estimate calibration error are suboptimal---we prove that an alternative estimator introduced in the meteorological community requires fewer samples ($O(\sqrt{B})$ instead of $O(B)$). We validate our approach with multiclass calibration experiments on CIFAR-10 and ImageNet, where we obtain a 35\% lower calibration error than histogram binning and, unlike scaling methods, guarantees on true calibration.