# Confidence Calibration with Bounded Error Using Transformations

arXiv: https://arxiv.org/abs/2102.12680 · HTML: https://mlsanity.com/paper/2102.12680/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 32 references that are in the map.
- First posted on arXiv 25 Feb 2021.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [YOLOv3: An Incremental Improvement](https://mlsanity.com/paper/1804.02767/) (2018)
- [YOLOv4: Optimal Speed and Accuracy of Object Detection](https://mlsanity.com/paper/2004.10934/) (2020)
- [Deep Networks with Stochastic Depth](https://mlsanity.com/paper/1603.09382/) (2016)
- [Measuring Calibration in Deep Learning](https://mlsanity.com/paper/1904.01685/) (2019)
- [Beyond temperature scaling: Obtaining well-calibrated multiclass probabilities with Dirichlet calibration](https://mlsanity.com/paper/1910.12656/) (2019)
- [Verified Uncertainty Calibration](https://mlsanity.com/paper/1909.10155/) (2019)
- [Mix-n-Match: Ensemble and Compositional Methods for Uncertainty Calibration in Deep Learning](https://mlsanity.com/paper/2003.07329/) (2020)
- [Calibration of Neural Networks using Splines](https://mlsanity.com/paper/2006.12800/) (2020)
- [Intra Order-preserving Functions for Calibration of Multi-Class Neural Networks](https://mlsanity.com/paper/2003.06820/) (2020)
- [Deep Speaker: an End-to-End Neural Speaker Embedding System](https://mlsanity.com/paper/1705.02304/) (2017)
- [Non-Parametric Calibration for Classification](https://mlsanity.com/paper/1906.04933/) (2019)
- [Multi-Class Uncertainty Calibration via Mutual Information Maximization-based Binning](https://mlsanity.com/paper/2006.13092/) (2020)
- [Learning for Single-Shot Confidence Calibration in Deep Neural Networks through Stochastic Inferences](https://mlsanity.com/paper/1809.10877/) (2018)
- [PAC Confidence Predictions for Deep Neural Network Classifiers](https://mlsanity.com/paper/2011.00716/) (2020)
- [Calibrating Deep Convolutional Gaussian Processes](https://mlsanity.com/paper/1805.10522/) (2018)
- [Classification Confidence Estimation with Test-Time Data-Augmentation](https://mlsanity.com/paper/2006.16705/) (2020)
- [Improving Classifier Confidence using Lossy Label-Invariant Transformations](https://mlsanity.com/paper/2011.04182/) (2020)

## Abstract (arXiv)

As machine learning techniques become widely adopted in new domains, especially in safety-critical systems such as autonomous vehicles, it is crucial to provide accurate output uncertainty estimation. As a result, many approaches have been proposed to calibrate neural networks to accurately estimate the likelihood of misclassification. However, while these methods achieve low calibration error, there is space for further improvement, especially in large-dimensional settings such as ImageNet. In this paper, we introduce a calibration algorithm, named Hoki, that works by applying random transformations to the neural network logits. We provide a sufficient condition for perfect calibration based on the number of label prediction changes observed after applying the transformations. We perform experiments on multiple datasets and show that the proposed approach generally outperforms state-of-the-art calibration algorithms across multiple datasets and models, especially on the challenging ImageNet dataset. Finally, Hoki is scalable as well, as it requires comparable execution time to that of temperature scaling.