# Mitigating Bias in Calibration Error Estimation

arXiv: https://arxiv.org/abs/2012.08668 · HTML: https://mlsanity.com/paper/2012.08668/

## Key facts

- Cited by 101 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Dec 2020.

## Built on by (most cited first, 30 of 101)

- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Revisiting the Calibration of Modern Neural Networks](https://mlsanity.com/paper/2106.07998/) (2021)
- [Document Understanding Dataset and Evaluation (DUDE)](https://mlsanity.com/paper/2305.08455/) (2023)
- [Soft Calibration Objectives for Neural Networks](https://mlsanity.com/paper/2108.00106/) (2021)
- [Calibration in Deep Learning: A Survey of the State-of-the-Art](https://mlsanity.com/paper/2308.01222/) (2023)
- [Human alignment of neural network representations](https://mlsanity.com/paper/2211.01201/) (2022)
- [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)
- [Smooth ECE: Principled Reliability Diagrams via Kernel Smoothing](https://mlsanity.com/paper/2309.12236/) (2023)
- [No One Representation to Rule Them All: Overlapping Features of Training Methods](https://mlsanity.com/paper/2110.12899/) (2021)
- [Uncertainty Estimation by Fisher Information-based Evidential Deep Learning](https://mlsanity.com/paper/2303.02045/) (2023)
- [A Unifying Theory of Distance from Calibration](https://mlsanity.com/paper/2211.16886/) (2022)
- [Conformal Prediction for Natural Language Processing: A Survey](https://mlsanity.com/paper/2405.01976/) (2024)
- [Sample-dependent Adaptive Temperature Scaling for Improved Calibration](https://mlsanity.com/paper/2207.06211/) (2022)
- [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)
- [von Mises-Fisher Loss: An Exploration of Embedding Geometries for Supervised Learning](https://mlsanity.com/paper/2103.15718/) (2021)
- [Calibrated Selective Classification](https://mlsanity.com/paper/2208.12084/) (2022)
- [Dual Focal Loss for Calibration](https://mlsanity.com/paper/2305.13665/) (2023)
- [Metrics of calibration for probabilistic predictions](https://mlsanity.com/paper/2205.09680/) (2022)
- [Beyond calibration: estimating the grouping loss of modern neural networks](https://mlsanity.com/paper/2210.16315/) (2022)
- [AdaFocal: Calibration-aware Adaptive Focal Loss](https://mlsanity.com/paper/2211.11838/) (2022)
- [LLMs Are Biased Towards Output Formats! Systematically Evaluating and Mitigating Output Format Bias of LLMs](https://mlsanity.com/paper/2408.08656/) (2024)
- [T-Cal: An optimal test for the calibration of predictive models](https://mlsanity.com/paper/2203.01850/) (2022)
- [A Survey on the Honesty of Large Language Models](https://mlsanity.com/paper/2409.18786/) (2024)
- [Mitigating the Risk of Health Inequity Exacerbated by Large Language Models](https://mlsanity.com/paper/2410.05180/) (2024)
- [Understanding Model Calibration -- A gentle introduction and visual exploration of calibration and the expected calibration error (ECE)](https://mlsanity.com/paper/2501.19047/) (2025)
- [Rethinking Early Stopping: Refine, Then Calibrate](https://mlsanity.com/paper/2501.19195/) (2025)
- [Trustworthy and Practical AI for Healthcare: A Guided Deferral System with Large Language Models](https://mlsanity.com/paper/2406.07212/) (2024)

## Abstract (arXiv)

For an AI system to be reliable, the confidence it expresses in its decisions must match its accuracy. To assess the degree of match, examples are typically binned by confidence and the per-bin mean confidence and accuracy are compared. Most research in calibration focuses on techniques to reduce this empirical measure of calibration error, ECE_bin. We instead focus on assessing statistical bias in this empirical measure, and we identify better estimators. We propose a framework through which we can compute the bias of a particular estimator for an evaluation data set of a given size. The framework involves synthesizing model outputs that have the same statistics as common neural architectures on popular data sets. We find that binning-based estimators with bins of equal mass (number of instances) have lower bias than estimators with bins of equal width. Our results indicate two reliable calibration-error estimators: the debiased estimator (Brocker, 2012; Ferro and Fricker, 2012) and a method we propose, ECE_sweep, which uses equal-mass bins and chooses the number of bins to be as large as possible while preserving monotonicity in the calibration function. With these estimators, we observe improvements in the effectiveness of recalibration methods and in the detection of model miscalibration.