# Optimal Transport for Multi-source Domain Adaptation under Target Shift

arXiv: https://arxiv.org/abs/1803.04899 · HTML: https://mlsanity.com/paper/1803.04899/

## Key facts

- Cited by 68 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Mar 2018.

## Built on by (most cited first, 30 of 68)

- [Plugin Estimation of Smooth Optimal Transport Maps](https://mlsanity.com/paper/2107.12364/) (2021)
- [Recent Advances in Optimal Transport for Machine Learning](https://mlsanity.com/paper/2306.16156/) (2023)
- [Domain Adaptation for Time Series Under Feature and Label Shifts](https://mlsanity.com/paper/2302.03133/) (2023)
- [Neural Optimal Transport with General Cost Functionals](https://mlsanity.com/paper/2205.15403/) (2022)
- [Understanding Gradual Domain Adaptation: Improved Analysis, Optimal Path and Beyond](https://mlsanity.com/paper/2204.08200/) (2022)
- [SoLar: Sinkhorn Label Refinery for Imbalanced Partial-Label Learning](https://mlsanity.com/paper/2209.10365/) (2022)
- [Meta Optimal Transport](https://mlsanity.com/paper/2206.05262/) (2022)
- [Transport-based Counterfactual Models](https://mlsanity.com/paper/2108.13025/) (2021)
- [Scalable Optimal Transport Methods in Machine Learning: A Contemporary Survey](https://mlsanity.com/paper/2305.05080/) (2023)
- [Aggregating From Multiple Target-Shifted Sources](https://mlsanity.com/paper/2105.04051/) (2021)
- [PatchCT: Aligning Patch Set and Label Set with Conditional Transport for Multi-Label Image Classification](https://mlsanity.com/paper/2307.09066/) (2023)
- [Mapping conditional distributions for domain adaptation under generalized target shift](https://mlsanity.com/paper/2110.15057/) (2021)
- [Gradual Domain Adaptation: Theory and Algorithms](https://mlsanity.com/paper/2310.13852/) (2023)
- [Data Valuation and Detections in Federated Learning](https://mlsanity.com/paper/2311.05304/) (2023)
- [On Learning Domain-Invariant Representations for Transfer Learning with Multiple Sources](https://mlsanity.com/paper/2111.13822/) (2021)
- [Wasserstein Barycenter-based Model Fusion and Linear Mode Connectivity of Neural Networks](https://mlsanity.com/paper/2210.06671/) (2022)
- [Limitations of Post-Hoc Feature Alignment for Robustness](https://mlsanity.com/paper/2103.05898/) (2021)
- [Secure Domain Adaptation with Multiple Sources](https://mlsanity.com/paper/2106.12124/) (2021)
- [OTAdapt: Optimal Transport-based Approach For Unsupervised Domain Adaptation](https://mlsanity.com/paper/2205.10738/) (2022)
- [Discovering Fine-Grained Visual-Concept Relations by Disentangled Optimal Transport Concept Bottleneck Models](https://mlsanity.com/paper/2505.07209/) (2025)
- [Learning to Rematch Mismatched Pairs for Robust Cross-Modal Retrieval](https://mlsanity.com/paper/2403.05105/) (2024)
- [Hierarchical Optimal Transport for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2112.02073/) (2021)
- [Measure Estimation in the Barycentric Coding Model](https://mlsanity.com/paper/2201.12195/) (2022)
- [InfoOT: Information Maximizing Optimal Transport](https://mlsanity.com/paper/2210.03164/) (2022)
- [More is Better: Deep Domain Adaptation with Multiple Sources](https://mlsanity.com/paper/2405.00749/) (2024)
- [Learning Gradients of Convex Functions with Monotone Gradient Networks](https://mlsanity.com/paper/2301.10862/) (2023)
- [Algorithm-Dependent Bounds for Representation Learning of Multi-Source Domain Adaptation](https://mlsanity.com/paper/2304.02064/) (2023)
- [Unsupervised Cross-Domain Image Retrieval via Prototypical Optimal Transport](https://mlsanity.com/paper/2402.18411/) (2024)
- [Transport and Merge: Cross-Architecture Merging for Large Language Models](https://mlsanity.com/paper/2602.05495/) (2026)
- [Unbalanced CO-Optimal Transport](https://mlsanity.com/paper/2205.14923/) (2022)

## Abstract (arXiv)

In this paper, we propose to tackle the problem of reducing discrepancies between multiple domains referred to as multi-source domain adaptation and consider it under the target shift assumption: in all domains we aim to solve a classification problem with the same output classes, but with labels' proportions differing across them. This problem, generally ignored in the vast majority papers on domain adaptation papers, is nevertheless critical in real-world applications, and we theoretically show its impact on the adaptation success. To address this issue, we design a method based on optimal transport, a theory that has been successfully used to tackle adaptation problems in machine learning. Our method performs multi-source adaptation and target shift correction simultaneously by learning the class probabilities of the unlabeled target sample and the coupling allowing to align two (or more) probability distributions. Experiments on both synthetic and real-world data related to satellite image segmentation task show the superiority of the proposed method over the state-of-the-art.