# Unsupervised Learning under Latent Label Shift

arXiv: https://arxiv.org/abs/2207.13179 · HTML: https://mlsanity.com/paper/2207.13179/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 94 references that are in the map.
- First posted on arXiv 26 Jul 2022.

## Builds on (most cited first, 30 of 32)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Unsupervised Representation Learning by Predicting Image Rotations](https://mlsanity.com/paper/1803.07728/) (2018)
- [Unsupervised Learning of Visual Representations by Solving Jigsaw Puzzles](https://mlsanity.com/paper/1603.09246/) (2016)
- [Unsupervised Visual Representation Learning by Context Prediction](https://mlsanity.com/paper/1505.05192/) (2015)
- [Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels](https://mlsanity.com/paper/1804.06872/) (2018)
- [Deep Clustering for Unsupervised Learning of Visual Features](https://mlsanity.com/paper/1807.05520/) (2018)
- [DivideMix: Learning with Noisy Labels as Semi-supervised Learning](https://mlsanity.com/paper/2002.07394/) (2020)
- [Making Deep Neural Networks Robust to Label Noise: a Loss Correction Approach](https://mlsanity.com/paper/1609.03683/) (2016)
- [Domain Generalization via Invariant Feature Representation](https://mlsanity.com/paper/1301.2115/) (2013)
- [Early-Learning Regularization Prevents Memorization of Noisy Labels](https://mlsanity.com/paper/2007.00151/) (2020)
- [Detecting and Correcting for Label Shift with Black Box Predictors](https://mlsanity.com/paper/1802.03916/) (2018)
- [SCAN: Learning to Classify Images without Labels](https://mlsanity.com/paper/2005.12320/) (2020)
- [Unsupervised Label Noise Modeling and Loss Correction](https://mlsanity.com/paper/1904.11238/) (2019)
- [Training Deep Neural Networks on Noisy Labels with Bootstrapping](https://mlsanity.com/paper/1412.6596/) (2014)
- [Joint Optimization Framework for Learning with Noisy Labels](https://mlsanity.com/paper/1803.11364/) (2018)
- [Learning from positive and unlabeled data: a survey](https://mlsanity.com/paper/1811.04820/) (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)
- [Robust Training under Label Noise by Over-parameterization](https://mlsanity.com/paper/2202.14026/) (2022)
- [Mixture Proportion Estimation and PU Learning: A Modern Approach](https://mlsanity.com/paper/2111.00980/) (2021)
- [Improving Unsupervised Image Clustering With Robust Learning](https://mlsanity.com/paper/2012.11150/) (2020)
- [Class-prior Estimation for Learning from Positive and Unlabeled Data](https://mlsanity.com/paper/1611.01586/) (2016)
- [Boosting Co-teaching with Compression Regularization for Label Noise](https://mlsanity.com/paper/2104.13766/) (2021)
- [Learning from Label Proportions by Learning with Label Noise](https://mlsanity.com/paper/2203.02496/) (2022)
- [Anchor-Free Correlated Topic Modeling: Identifiability and Algorithm](https://mlsanity.com/paper/1611.05010/) (2016)
- [Consistent Estimation of Identifiable Nonparametric Mixture Models from Grouped Observations](https://mlsanity.com/paper/2006.07459/) (2020)

## Built on by (most cited first, 9 of 9)

- [Subspace Identification for Multi-Source Domain Adaptation](https://mlsanity.com/paper/2310.04723/) (2023)
- [RLSbench: Domain Adaptation Under Relaxed Label Shift](https://mlsanity.com/paper/2302.03020/) (2023)
- [Any-Shift Prompting for Generalization over Distributions](https://mlsanity.com/paper/2402.10099/) (2024)
- [Online Label Shift: Optimal Dynamic Regret meets Practical Algorithms](https://mlsanity.com/paper/2305.19570/) (2023)
- [ELSA: Efficient Label Shift Adaptation through the Lens of Semiparametric Models](https://mlsanity.com/paper/2305.19123/) (2023)
- [Complementary Benefits of Contrastive Learning and Self-Training Under Distribution Shift](https://mlsanity.com/paper/2312.03318/) (2023)
- [A General Representation-Based Approach to Multi-Source Domain Adaptation](https://mlsanity.com/paper/2604.23790/) (2026)
- [Addressing Label Shift in Distributed Learning via Entropy Regularization](https://mlsanity.com/paper/2502.02544/) (2025)
- [Time Series Domain Adaptation via Latent Invariant Causal Mechanism](https://mlsanity.com/paper/2502.16637/) (2025)

## Abstract (arXiv)

What sorts of structure might enable a learner to discover classes from unlabeled data? Traditional approaches rely on feature-space similarity and heroic assumptions on the data. In this paper, we introduce unsupervised learning under Latent Label Shift (LLS), where we have access to unlabeled data from multiple domains such that the label marginals pd(y) can shift across domains but the class conditionals p(x|y) do not. This work instantiates a new principle for identifying classes: elements that shift together group together. For finite input spaces, we establish an isomorphism between LLS and topic modeling: inputs correspond to words, domains to documents, and labels to topics. Addressing continuous data, we prove that when each label's support contains a separable region, analogous to an anchor word, oracle access to p(d|x) suffices to identify pd(y) and pd(y|x) up to permutation. Thus motivated, we introduce a practical algorithm that leverages domain-discriminative models as follows: (i) push examples through domain discriminator p(d|x); (ii) discretize the data by clustering examples in p(d|x) space; (iii) perform non-negative matrix factorization on the discrete data; (iv) combine the recovered p(y|d) with the discriminator outputs p(d|x) to compute pd(y|x) ; forall d. With semi-synthetic experiments, we show that our algorithm can leverage domain information to improve upon competitive unsupervised classification methods. We reveal a failure mode of standard unsupervised classification methods when feature-space similarity does not indicate true groupings, and show empirically that our method better handles this case. Our results establish a deep connection between distribution shift and topic modeling, opening promising lines for future work.