# Optimal Transport for Domain Adaptation

arXiv: https://arxiv.org/abs/1507.00504 · HTML: https://mlsanity.com/paper/1507.00504/

## Key facts

- Cited by 463 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jul 2015.

## Built on by (most cited first, 30 of 463)

- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Unbalanced minibatch Optimal Transport; applications to Domain Adaptation](https://mlsanity.com/paper/2103.03606/) (2021)
- [Entropic estimation of optimal transport maps](https://mlsanity.com/paper/2109.12004/) (2021)
- [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)
- [Minibatch optimal transport distances; analysis and applications](https://mlsanity.com/paper/2101.01792/) (2021)
- [Editing a classifier by rewriting its prediction rules](https://mlsanity.com/paper/2112.01008/) (2021)
- [OTCE: A Transferability Metric for Cross-Domain Cross-Task Representations](https://mlsanity.com/paper/2103.13843/) (2021)
- [Patch-Mix Transformer for Unsupervised Domain Adaptation: A Game Perspective](https://mlsanity.com/paper/2303.13434/) (2023)
- [Rates of Estimation of Optimal Transport Maps using Plug-in Estimators via Barycentric Projections](https://mlsanity.com/paper/2107.01718/) (2021)
- [Domain Adversarial Neural Networks for Domain Generalization: When It Works and How to Improve](https://mlsanity.com/paper/2102.03924/) (2021)
- [Unbalanced Optimal Transport, from Theory to Numerics](https://mlsanity.com/paper/2211.08775/) (2022)
- [Unbalanced Feature Transport for Exemplar-based Image Translation](https://mlsanity.com/paper/2106.10482/) (2021)
- [Improving Mini-batch Optimal Transport via Partial Transportation](https://mlsanity.com/paper/2108.09645/) (2021)
- [Generative Modeling through the Semi-dual Formulation of Unbalanced Optimal Transport](https://mlsanity.com/paper/2305.14777/) (2023)
- [Neural Monge Map estimation and its applications](https://mlsanity.com/paper/2106.03812/) (2021)
- [BMD: A General Class-balanced Multicentric Dynamic Prototype Strategy for Source-free Domain Adaptation](https://mlsanity.com/paper/2204.02811/) (2022)
- [Co-Transport for Class-Incremental Learning](https://mlsanity.com/paper/2107.12654/) (2021)
- [Automatic Text Evaluation through the Lens of Wasserstein Barycenters](https://mlsanity.com/paper/2108.12463/) (2021)
- [Sinkhorn Distributionally Robust Optimization](https://mlsanity.com/paper/2109.11926/) (2021)
- [Few-shot Segmentation with Optimal Transport Matching and Message Flow](https://mlsanity.com/paper/2108.08518/) (2021)
- [Data Efficient Language-supervised Zero-shot Recognition with Optimal Transport Distillation](https://mlsanity.com/paper/2112.09445/) (2021)
- [Neural Optimal Transport with General Cost Functionals](https://mlsanity.com/paper/2205.15403/) (2022)
- [A Survey on Optimal Transport for Machine Learning: Theory and Applications](https://mlsanity.com/paper/2106.01963/) (2021)
- [INTERN: A New Learning Paradigm Towards General Vision](https://mlsanity.com/paper/2111.08687/) (2021)
- [PATS: Patch Area Transportation with Subdivision for Local Feature Matching](https://mlsanity.com/paper/2303.07700/) (2023)
- [Debias Coarsely, Sample Conditionally: Statistical Downscaling through Optimal Transport and Probabilistic Diffusion Models](https://mlsanity.com/paper/2305.15618/) (2023)
- [Understanding Gradual Domain Adaptation: Improved Analysis, Optimal Path and Beyond](https://mlsanity.com/paper/2204.08200/) (2022)
- [The Monge Gap: A Regularizer to Learn All Transport Maps](https://mlsanity.com/paper/2302.04953/) (2023)
- [Optimal Transport for Treatment Effect Estimation](https://mlsanity.com/paper/2310.18286/) (2023)

## Abstract (arXiv)

Domain adaptation from one data space (or domain) to another is one of the most challenging tasks of modern data analytics. If the adaptation is done correctly, models built on a specific data space become more robust when confronted to data depicting the same semantic concepts (the classes), but observed by another observation system with its own specificities. Among the many strategies proposed to adapt a domain to another, finding a common representation has shown excellent properties: by finding a common representation for both domains, a single classifier can be effective in both and use labelled samples from the source domain to predict the unlabelled samples of the target domain. In this paper, we propose a regularized unsupervised optimal transportation model to perform the alignment of the representations in the source and target domains. We learn a transportation plan matching both PDFs, which constrains labelled samples in the source domain to remain close during transport. This way, we exploit at the same time the few labeled information in the source and the unlabelled distributions observed in both domains. Experiments in toy and challenging real visual adaptation examples show the interest of the method, that consistently outperforms state of the art approaches.