# Bayesian-based Online Label Shift Estimation with Dynamic Dirichlet Priors

arXiv: https://arxiv.org/abs/2511.18615 · HTML: https://mlsanity.com/paper/2511.18615/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 51 references that are in the map.
- First posted on arXiv 23 Nov 2025.

## Builds on (most cited first, 21 of 21)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Learning Imbalanced Datasets with Label-Distribution-Aware Margin Loss](https://mlsanity.com/paper/1906.07413/) (2019)
- [Large-Scale Long-Tailed Recognition in an Open World](https://mlsanity.com/paper/1904.05160/) (2019)
- [Detecting and Correcting for Label Shift with Black Box Predictors](https://mlsanity.com/paper/1802.03916/) (2018)
- [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)
- [Reliable Conflictive Multi-View Learning](https://mlsanity.com/paper/2402.16897/) (2024)
- [Online Adaptation to Label Distribution Shift](https://mlsanity.com/paper/2107.04520/) (2021)
- [Adapting to Online Label Shift with Provable Guarantees](https://mlsanity.com/paper/2207.02121/) (2022)
- [Towards Explaining Distribution Shifts](https://mlsanity.com/paper/2210.10275/) (2022)
- [Active Learning under Label Shift](https://mlsanity.com/paper/2007.08479/) (2020)
- [Test-time Adaptation with Calibration of Medical Image Classification Nets for Label Distribution Shift](https://mlsanity.com/paper/2207.00769/) (2022)
- [Online Label Shift: Optimal Dynamic Regret meets Practical Algorithms](https://mlsanity.com/paper/2305.19570/) (2023)
- [Tensor Decompositions for Identifying Directed Graph Topologies and Tracking Dynamic Networks](https://mlsanity.com/paper/1610.08189/) (2016)
- [Cost-Effective Retraining of Machine Learning Models](https://mlsanity.com/paper/2310.04216/) (2023)
- [Activity Detection for Massive Connectivity in Cell-free Networks with Unknown Large-scale Fading, Channel Statistics, Noise Variance, and Activity Probability: A Bayesian Approach](https://mlsanity.com/paper/2401.16775/) (2024)
- [Text Classification Under Class Distribution Shift: A Survey](https://mlsanity.com/paper/2502.12965/) (2025)
- [Online Inference for Mixture Model of Streaming Graph Signals with Non-White Excitation](https://mlsanity.com/paper/2207.14019/) (2022)
- [Online Graph Topology Learning via Time-Vertex Adaptive Filters: From Theory to Cardiac Fibrillation](https://mlsanity.com/paper/2411.01567/) (2024)
- [Robotic Long-Horizon Manipulation with Bayesian Non-parametric Skill Priors](https://mlsanity.com/paper/2503.21975/) (2025)

## Built on by (most cited first, 1 of 1)

- [Geometry-Aware Bayesian Quantification via Compositional Data Analysis](https://mlsanity.com/paper/2607.04977/) (2026)

## Abstract (arXiv)

Label shift, a prevalent challenge in supervised learning, arises when the class prior distribution of test data differs from that of training data, leading to significant degradation in classifier performance. To accurately estimate the test priors and enhance classification accuracy, we propose a Bayesian framework for label shift estimation, termed Full Maximum A Posterior Label Shift (FMAPLS), along with its online version, online-FMAPLS. Leveraging batch and online Expectation-Maximization (EM) algorithms, these methods jointly and dynamically optimize Dirichlet hyperparameters boldsymbolα and class priors boldsymbolπ, thereby overcoming the rigid constraints of the existing Maximum A Posterior Label Shift (MAPLS) approach. Moreover, we introduce a linear surrogate function (LSF) to replace gradient-based hyperparameter updates, yielding closed-form solutions that reduce computational complexity while retaining asymptotic equivalence. The online variant substitutes the batch E-step with a stochastic approximation, enabling real-time adaptation to streaming data. Furthermore, our theoretical analysis reveals a fundamental trade-off between online convergence rate and estimation accuracy. Extensive experiments on CIFAR100 and ImageNet datasets under shuffled long-tail and Dirichlet test priors demonstrate that FMAPLS and online-FMAPLS respectively achieve up to 40% and 12% lower KL divergence and substantial improvements in post-shift accuracy over state-of-the-art baselines, particularly under severe class imbalance and distributional uncertainty. These results confirm the robustness, scalability, and suitability of the proposed methods for large-scale and dynamic learning scenarios.