# Label Shift Estimation With Incremental Prior Update

arXiv: https://arxiv.org/abs/2604.01651 · HTML: https://mlsanity.com/paper/2604.01651/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 27 references that are in the map.
- First posted on arXiv 2 Apr 2026.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Detecting and Correcting for Label Shift with Black Box Predictors](https://mlsanity.com/paper/1802.03916/) (2018)
- [Beyond temperature scaling: Obtaining well-calibrated multiclass probabilities with Dirichlet calibration](https://mlsanity.com/paper/1910.12656/) (2019)
- [What is the Effect of Importance Weighting in Deep Learning?](https://mlsanity.com/paper/1812.03372/) (2018)
- [CReST: A Class-Rebalancing Self-Training Framework for Imbalanced Semi-Supervised Learning](https://mlsanity.com/paper/2102.09559/) (2021)
- [Domain Adaptation with Conditional Distribution Matching and Generalized Label Shift](https://mlsanity.com/paper/2003.04475/) (2020)
- [Regularized Learning for Domain Adaptation under Label Shifts](https://mlsanity.com/paper/1903.09734/) (2019)
- [A Unified View of Label Shift Estimation](https://mlsanity.com/paper/2003.07554/) (2020)
- [Distribution Aligning Refinery of Pseudo-label for Imbalanced Semi-supervised Learning](https://mlsanity.com/paper/2007.08844/) (2020)
- [Classifier Calibration: A survey on how to assess and improve predicted class probabilities](https://mlsanity.com/paper/2112.10327/) (2021)
- [Generalized Logit Adjustment: Calibrating Fine-tuned Models by Removing Label Bias in Foundation Models](https://mlsanity.com/paper/2310.08106/) (2023)
- [Online Label Shift: Optimal Dynamic Regret meets Practical Algorithms](https://mlsanity.com/paper/2305.19570/) (2023)

## Abstract (arXiv)

An assumption often made in supervised learning is that the training and testing sets have the same label distribution. However, in real-life scenarios, this assumption rarely holds. For example, medical diagnosis result distributions change over time and across locations; fraud detection models must adapt as patterns of fraudulent activity shift; the category distribution of social media posts changes based on trending topics and user demographics. In the task of label shift estimation, the goal is to estimate the changing label distribution pt(y) in the testing set, assuming the likelihood p(x|y) does not change, implying no concept drift. In this paper, we propose a new approach for post-hoc label shift estimation, unlike previous methods that perform moment matching with confusion matrix estimated from a validation set or maximize the likelihood of the new data with an expectation-maximization algorithm. We aim to incrementally update the prior on each sample, adjusting each posterior for more accurate label shift estimation. The proposed method is based on intuitive assumptions on classifiers that are generally true for modern probabilistic classifiers. The proposed method relies on a weaker notion of calibration compared to other methods. As a post-hoc approach for label shift estimation, the proposed method is versatile and can be applied to any black-box probabilistic classifier. Experiments on CIFAR-10 and MNIST show that the proposed method consistently outperforms the current state-of-the-art maximum likelihood-based methods under different calibrations and varying intensities of label shift.