# Optimal Transport for Conditional Domain Matching and Label Shift

arXiv: https://arxiv.org/abs/2006.08161 · HTML: https://mlsanity.com/paper/2006.08161/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2020.

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

- [Plugin Estimation of Smooth Optimal Transport Maps](https://mlsanity.com/paper/2107.12364/) (2021)
- [Conditional Wasserstein Distances with Applications in Bayesian OT Flow Matching](https://mlsanity.com/paper/2403.18705/) (2024)
- [Learning to Re-weight Examples with Optimal Transport for Imbalanced Classification](https://mlsanity.com/paper/2208.02951/) (2022)
- [Mapping conditional distributions for domain adaptation under generalized target shift](https://mlsanity.com/paper/2110.15057/) (2021)
- [Data Valuation and Detections in Federated Learning](https://mlsanity.com/paper/2311.05304/) (2023)
- [Generalized Universal Domain Adaptation with Generative Flow Networks](https://mlsanity.com/paper/2305.04466/) (2023)
- [Explanatory Model Monitoring to Understand the Effects of Feature Shifts on Performance](https://mlsanity.com/paper/2408.13648/) (2024)
- [Y-Diagonal Couplings: Approximating Posteriors with Conditional Wasserstein Distances](https://mlsanity.com/paper/2310.13433/) (2023)
- [Connecting sufficient conditions for domain adaptation: source-guided uncertainty, relaxed divergences and discrepancy localization](https://mlsanity.com/paper/2203.05076/) (2022)
- [Learning representations that are closed-form Monge mapping optimal with application to domain adaptation](https://mlsanity.com/paper/2305.07500/) (2023)
- [OT-Net: A Reusable Neural Optimal Transport Solver](https://mlsanity.com/paper/2306.08233/) (2023)
- [When Invariant Representation Learning Meets Label Shift: Insufficiency and Theoretical Insights](https://mlsanity.com/paper/2406.16608/) (2024)
- [Sparse Partial Optimal Transport via Quadratic Regularization](https://mlsanity.com/paper/2508.08476/) (2025)
- [Connecting adversarial attacks and optimal transport for domain adaptation](https://mlsanity.com/paper/2205.15424/) (2022)
- [Source-free Domain Adaptation Requires Penalized Diversity](https://mlsanity.com/paper/2304.02798/) (2023)
- [On the impact of measure pre-conditionings on general parametric ML models and transfer learning via domain adaptation](https://mlsanity.com/paper/2403.02432/) (2024)
- [Theory-inspired Label Shift Adaptation via Aligned Distribution Mixture](https://mlsanity.com/paper/2411.02047/) (2024)
- [A Generalized Label Shift Perspective for Cross-Domain Gaze Estimation](https://mlsanity.com/paper/2505.13043/) (2025)
- [Investigating Mask-aware Prototype Learning for Tabular Anomaly Detection](https://mlsanity.com/paper/2506.02757/) (2025)
- [OTROPE: Optimal Transport-based Robust Off-policy Evaluation for Large Language Models](https://mlsanity.com/paper/2609.36264/) (2026)

## Abstract (arXiv)

We address the problem of unsupervised domain adaptation under the setting of generalized target shift (joint class-conditional and label shifts). For this framework, we theoretically show that, for good generalization, it is necessary to learn a latent representation in which both marginals and class-conditional distributions are aligned across domains. For this sake, we propose a learning problem that minimizes importance weighted loss in the source domain and a Wasserstein distance between weighted marginals. For a proper weighting, we provide an estimator of target label proportion by blending mixture estimation and optimal matching by optimal transport. This estimation comes with theoretical guarantees of correctness under mild assumptions. Our experimental results show that our method performs better on average than competitors across a range domain adaptation problems including digits,VisDA and Office. Code for this paper is available at urlhttps://github.com/arakotom/marsdomainadaptation.