# Generalized Label Shift Correction via Minimum Uncertainty Principle: Theory and Algorithm

arXiv: https://arxiv.org/abs/2202.13043 · HTML: https://mlsanity.com/paper/2202.13043/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 53 references that are in the map.
- First posted on arXiv 26 Feb 2022.

## Builds on (most cited first, 25 of 25)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Unsupervised Domain Adaptation by Backpropagation](https://mlsanity.com/paper/1409.7495/) (2014)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [Deep Transfer Learning with Joint Adaptation Networks](https://mlsanity.com/paper/1605.06636/) (2016)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [VisDA: The Visual Domain Adaptation Challenge](https://mlsanity.com/paper/1710.06924/) (2017)
- [Detecting and Correcting for Label Shift with Black Box Predictors](https://mlsanity.com/paper/1802.03916/) (2018)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [What is the Effect of Importance Weighting in Deep Learning?](https://mlsanity.com/paper/1812.03372/) (2018)
- [Mind the Class Weight Bias: Weighted Maximum Mean Discrepancy for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1705.00609/) (2017)
- [Partial Adversarial Domain Adaptation](https://mlsanity.com/paper/1808.04205/) (2018)
- [Domain Adaptation with Conditional Distribution Matching and Generalized Label Shift](https://mlsanity.com/paper/2003.04475/) (2020)
- [Importance Weighted Adversarial Nets for Partial Domain Adaptation](https://mlsanity.com/paper/1803.09210/) (2018)
- [Learning to Transfer Examples for Partial Domain Adaptation](https://mlsanity.com/paper/1903.12230/) (2019)
- [A Measure-Theoretic Approach to Kernel Conditional Mean Embeddings](https://mlsanity.com/paper/2002.03689/) (2020)
- [Maximum Density Divergence for Domain Adaptation](https://mlsanity.com/paper/2004.12615/) (2020)
- [Unsupervised Reverse Domain Adaptation for Synthetic Medical Images via Adversarial Training](https://mlsanity.com/paper/1711.06606/) (2017)
- [Deep Residual Correction Network for Partial Domain Adaptation](https://mlsanity.com/paper/2004.04914/) (2020)
- [Unsupervised Domain Adaptation via Discriminative Manifold Propagation](https://mlsanity.com/paper/2008.10030/) (2020)
- [A Rigorous Theory of Conditional Mean Embeddings](https://mlsanity.com/paper/1912.00671/) (2019)
- [Conditional Bures Metric for Domain Adaptation](https://mlsanity.com/paper/2108.00302/) (2021)
- [Addressing Appearance Change in Outdoor Robotics with Adversarial Domain Adaptation](https://mlsanity.com/paper/1703.01461/) (2017)
- [Domain Adaptive Person Re-Identification via Camera Style Generation and Label Propagation](https://mlsanity.com/paper/1905.05382/) (2019)
- [Deep Spherical Manifold Gaussian Kernel for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2105.02089/) (2021)
- [Towards Uncovering the Intrinsic Data Structures for Unsupervised Domain Adaptation using Structurally Regularized Deep Clustering](https://mlsanity.com/paper/2012.04280/) (2020)

## Built on by (most cited first, 3 of 3)

- [Partial Domain Adaptation via Importance Sampling-based Shift Correction](https://mlsanity.com/paper/2507.20191/) (2025)
- [Addressing Label Shift in Distributed Learning via Entropy Regularization](https://mlsanity.com/paper/2502.02544/) (2025)
- [Locality-aware Private Class Identification for Domain Adaptation with Extreme Label Shift](https://mlsanity.com/paper/2605.05567/) (2026)

## Abstract (arXiv)

As a fundamental problem in machine learning, dataset shift induces a paradigm to learn and transfer knowledge under changing environment. Previous methods assume the changes are induced by covariate, which is less practical for complex real-world data. We consider the Generalized Label Shift (GLS), which provides an interpretable insight into the learning and transfer of desirable knowledge. Current GLS methods: 1) are not well-connected with the statistical learning theory; 2) usually assume the shifting conditional distributions will be matched with an implicit transformation, but its explicit modeling is unexplored. In this paper, we propose a conditional adaptation framework to deal with these challenges. From the perspective of learning theory, we prove that the generalization error of conditional adaptation is lower than previous covariate adaptation. Following the theoretical results, we propose the minimum uncertainty principle to learn conditional invariant transformation via discrepancy optimization. Specifically, we propose the textitconditional metric operator on Hilbert space to characterize the distinctness of conditional distributions. For finite observations, we prove that the empirical estimation is always well-defined and will converge to underlying truth as sample size increases. The results of extensive experiments demonstrate that the proposed model achieves competitive performance under different GLS scenarios.