# Minimax optimal approaches to the label shift problem in non-parametric settings

arXiv: https://arxiv.org/abs/2003.10443 · HTML: https://mlsanity.com/paper/2003.10443/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Mar 2020.

## Built on by (most cited first, 20 of 20)

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- [Pseudo-Labeling for Kernel Ridge Regression under Covariate Shift](https://mlsanity.com/paper/2302.10160/) (2023)
- [A transfer learning framework for weak-to-strong generalization](https://mlsanity.com/paper/2405.16236/) (2024)
- [Understanding new tasks through the lens of training data via exponential tilting](https://mlsanity.com/paper/2205.13577/) (2022)
- [ELSA: Efficient Label Shift Adaptation through the Lens of Semiparametric Models](https://mlsanity.com/paper/2305.19123/) (2023)
- [Provable Benefits of Unsupervised Pre-training and Transfer Learning via Single-Index Models](https://mlsanity.com/paper/2502.16849/) (2025)
- [Minimax And Adaptive Transfer Learning for Nonparametric Classification under Distributed Differential Privacy Constraints](https://mlsanity.com/paper/2406.20088/) (2024)
- [Adaptive transfer learning](https://mlsanity.com/paper/2106.04455/) (2021)
- [On Causality in Domain Adaptation and Semi-Supervised Learning: an Information-Theoretic Analysis for Parametric Models](https://mlsanity.com/paper/2205.04641/) (2022)
- [Undersampling is a Minimax Optimal Robustness Intervention in Nonparametric Classification](https://mlsanity.com/paper/2205.13094/) (2022)
- [Fixed-Gaussian Spectral Algorithms: Minimax Optimal Rates for Misspecified Learning and Transfer](https://mlsanity.com/paper/2501.10870/) (2025)
- [Late Fusion Multi-task Learning for Semiparametric Inference with Nuisance Parameters](https://mlsanity.com/paper/2507.07941/) (2025)
- [Importance Weighting Correction of Regularized Least-Squares for Target Shift](https://mlsanity.com/paper/2210.09709/) (2022)
- [Open Set Label Shift with Test Time Out-of-Distribution Reference](https://mlsanity.com/paper/2505.05868/) (2025)
- [Limitations of refinement methods for weak to strong generalization](https://mlsanity.com/paper/2508.17018/) (2025)
- [Addressing Distribution Shift in RTB Markets via Exponential Tilting](https://mlsanity.com/paper/2308.07424/) (2023)
- [An adaptive transfer learning perspective on classification in non-stationary environments](https://mlsanity.com/paper/2405.18091/) (2024)
- [Theory-inspired Label Shift Adaptation via Aligned Distribution Mixture](https://mlsanity.com/paper/2411.02047/) (2024)

## Abstract (arXiv)

We study the minimax rates of the label shift problem in non-parametric classification. In addition to the unsupervised setting in which the learner only has access to unlabeled examples from the target domain, we also consider the setting in which a small number of labeled examples from the target domain is available to the learner. Our study reveals a difference in the difficulty of the label shift problem in the two settings, and we attribute this difference to the availability of data from the target domain to estimate the class conditional distributions in the latter setting. We also show that a class proportion estimation approach is minimax rate-optimal in the unsupervised setting.