# Multiclass Calibration Assessment and Recalibration of Probability Predictions via the Linear Log Odds Calibration Function

arXiv: https://arxiv.org/abs/2602.18573 · HTML: https://mlsanity.com/paper/2602.18573/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 35 references that are in the map.
- First posted on arXiv 20 Feb 2026.

## Builds on (most cited first, 14 of 14)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Evaluating model calibration in classification](https://mlsanity.com/paper/1902.06977/) (2019)
- [Multivariate Confidence Calibration for Object Detection](https://mlsanity.com/paper/2004.13546/) (2020)
- [Calibration tests in multi-class classification: A unifying framework](https://mlsanity.com/paper/1910.11385/) (2019)
- [Classifier Calibration: A survey on how to assess and improve predicted class probabilities](https://mlsanity.com/paper/2112.10327/) (2021)
- [Adversarial Machine Learning in Image Classification: A Survey Towards the Defender's Perspective](https://mlsanity.com/paper/2009.03728/) (2020)
- [Understanding metric-related pitfalls in image analysis validation](https://mlsanity.com/paper/2302.01790/) (2023)
- [Estimating Expected Calibration Errors](https://mlsanity.com/paper/2109.03480/) (2021)
- [Binary Classifier Calibration using an Ensemble of Near Isotonic Regression Models](https://mlsanity.com/paper/1511.05191/) (2015)
- [Confidence Calibration of Classifiers with Many Classes](https://mlsanity.com/paper/2411.02988/) (2024)
- [Does deep learning model calibration improve performance in class-imbalanced medical image classification?](https://mlsanity.com/paper/2110.00918/) (2021)
- [Understanding Calibration of Deep Neural Networks for Medical Image Classification](https://mlsanity.com/paper/2309.13132/) (2023)
- [A proof of convergence of multi-class logistic regression network](https://mlsanity.com/paper/1903.12600/) (2019)

## Abstract (arXiv)

Machine-generated probability predictions are essential in modern classification tasks such as image classification. A model is well calibrated when its predicted probabilities correspond to observed event frequencies. Despite the need for multicategory recalibration methods, existing methods are limited to (i) comparing calibration between two or more models rather than directly assessing the calibration of a single model, (ii) requiring under-the-hood model access, e.g., accessing logit-scale predictions within the layers of a neural network, and (iii) providing output which is difficult for human analysts to understand. To overcome (i)-(iii), we propose Multicategory Linear Log Odds (MCLLO) recalibration, which (i) includes a likelihood ratio hypothesis test to assess calibration, (ii) does not require under-the-hood access to models and is thus applicable on a wide range of classification problems, and (iii) can be easily interpreted. We demonstrate the effectiveness of the MCLLO method through simulations and three real-world case studies involving image classification via convolutional neural network, obesity analysis via random forest, and ecology via regression modeling. We compare MCLLO to four comparator recalibration techniques utilizing both our hypothesis test and the existing calibration metric Expected Calibration Error to show that our method works well alone and in concert with other methods.