# Verified Uncertainty Calibration

arXiv: https://arxiv.org/abs/1909.10155 · HTML: https://mlsanity.com/paper/1909.10155/

## Key facts

- Cited by 309 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Sep 2019.

## Built on by (most cited first, 30 of 309)

- [Revisiting the Calibration of Modern Neural Networks](https://mlsanity.com/paper/2106.07998/) (2021)
- [Unsolved Problems in ML Safety](https://mlsanity.com/paper/2109.13916/) (2021)
- [Understanding Dataset Difficulty with V-Usable Information](https://mlsanity.com/paper/2110.08420/) (2021)
- [Large Legal Fictions: Profiling Legal Hallucinations in Large Language Models](https://mlsanity.com/paper/2401.01301/) (2024)
- [Document Understanding Dataset and Evaluation (DUDE)](https://mlsanity.com/paper/2305.08455/) (2023)
- [Evaluating ChatGPT's Information Extraction Capabilities: An Assessment of Performance, Explainability, Calibration, and Faithfulness](https://mlsanity.com/paper/2304.11633/) (2023)
- [Assessing Generalization of SGD via Disagreement](https://mlsanity.com/paper/2106.13799/) (2021)
- [What Large Language Models Know and What People Think They Know](https://mlsanity.com/paper/2401.13835/) (2024)
- [Task-Specific Skill Localization in Fine-tuned Language Models](https://mlsanity.com/paper/2302.06600/) (2023)
- [Distribution-free uncertainty quantification for classification under label shift](https://mlsanity.com/paper/2103.03323/) (2021)
- [Soft Calibration Objectives for Neural Networks](https://mlsanity.com/paper/2108.00106/) (2021)
- [TransMix: Attend to Mix for Vision Transformers](https://mlsanity.com/paper/2111.09833/) (2021)
- [Classifier Calibration: A survey on how to assess and improve predicted class probabilities](https://mlsanity.com/paper/2112.10327/) (2021)
- [Better Uncertainty Calibration via Proper Scores for Classification and Beyond](https://mlsanity.com/paper/2203.07835/) (2022)
- [Training Uncertainty-Aware Classifiers with Conformalized Deep Learning](https://mlsanity.com/paper/2205.05878/) (2022)
- [Trustworthy clinical AI solutions: a unified review of uncertainty quantification in deep learning models for medical image analysis](https://mlsanity.com/paper/2210.03736/) (2022)
- [Smooth ECE: Principled Reliability Diagrams via Kernel Smoothing](https://mlsanity.com/paper/2309.12236/) (2023)
- [When and How Mixup Improves Calibration](https://mlsanity.com/paper/2102.06289/) (2021)
- [Understanding metric-related pitfalls in image analysis validation](https://mlsanity.com/paper/2302.01790/) (2023)
- [Calibrating Language Models with Adaptive Temperature Scaling](https://mlsanity.com/paper/2409.19817/) (2024)
- [A Unifying Theory of Distance from Calibration](https://mlsanity.com/paper/2211.16886/) (2022)
- [Stochastic Concept Bottleneck Models](https://mlsanity.com/paper/2406.19272/) (2024)
- [SmoothMix: Training Confidence-calibrated Smoothed Classifiers for Certified Robustness](https://mlsanity.com/paper/2111.09277/) (2021)
- [A Stitch in Time Saves Nine: A Train-Time Regularizing Loss for Improved Neural Network Calibration](https://mlsanity.com/paper/2203.13834/) (2022)
- [Parameterized Temperature Scaling for Boosting the Expressive Power in Post-Hoc Uncertainty Calibration](https://mlsanity.com/paper/2102.12182/) (2021)
- [A Consistent and Differentiable Lp Canonical Calibration Error Estimator](https://mlsanity.com/paper/2210.07810/) (2022)
- [Top-label calibration and multiclass-to-binary reductions](https://mlsanity.com/paper/2107.08353/) (2021)
- [Distribution-free calibration guarantees for histogram binning without sample splitting](https://mlsanity.com/paper/2105.04656/) (2021)
- [PAC Prediction Sets Under Covariate Shift](https://mlsanity.com/paper/2106.09848/) (2021)
- [Rethinking Confidence Calibration for Failure Prediction](https://mlsanity.com/paper/2303.02970/) (2023)

## Abstract (arXiv)

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/ε2) samples, compared to O(1/ε2) 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 to reduce variance and then bins the function values to actually ensure calibration. This requires only O(1/ε2 + B) samples. Next, we show that we can estimate a model's calibration error more accurately using an estimator from the meteorological community---or equivalently measure its calibration error with fewer samples (O(√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. In these experiments, we also estimate the calibration error and ECE more accurately than the commonly used plugin estimators. We implement all these methods in a Python library: https://pypi.org/project/uncertainty-calibration