# Theoretical Analysis of Domain Adaptation with Optimal Transport

arXiv: https://arxiv.org/abs/1610.04420 · HTML: https://mlsanity.com/paper/1610.04420/

## Key facts

- Cited by 105 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Oct 2016.

## Built on by (most cited first, 30 of 105)

- [Reusing the Task-specific Classifier as a Discriminator: Discriminator-free Adversarial Domain Adaptation](https://mlsanity.com/paper/2204.03838/) (2022)
- [Recent Advances in Optimal Transport for Machine Learning](https://mlsanity.com/paper/2306.16156/) (2023)
- [Domain Adversarial Neural Networks for Domain Generalization: When It Works and How to Improve](https://mlsanity.com/paper/2102.03924/) (2021)
- [Meta-Learning Dynamics Forecasting Using Task Inference](https://mlsanity.com/paper/2102.10271/) (2021)
- [A Survey on Optimal Transport for Machine Learning: Theory and Applications](https://mlsanity.com/paper/2106.01963/) (2021)
- [Optimal Transport for Treatment Effect Estimation](https://mlsanity.com/paper/2310.18286/) (2023)
- [Scalable Optimal Transport Methods in Machine Learning: A Contemporary Survey](https://mlsanity.com/paper/2305.05080/) (2023)
- [Semi-Supervised Domain Adaptation with Source Label Adaptation](https://mlsanity.com/paper/2302.02335/) (2023)
- [Assessing Fairness in the Presence of Missing Data](https://mlsanity.com/paper/2112.04899/) (2021)
- [Cross-domain Activity Recognition via Substructural Optimal Transport](https://mlsanity.com/paper/2102.03353/) (2021)
- [An improved central limit theorem and fast convergence rates for entropic transportation costs](https://mlsanity.com/paper/2204.09105/) (2022)
- [Data Valuation and Detections in Federated Learning](https://mlsanity.com/paper/2311.05304/) (2023)
- [Cognitively Inspired Learning of Incremental Drifting Concepts](https://mlsanity.com/paper/2110.04662/) (2021)
- [Unsupervised Noise Adaptive Speech Enhancement by Discriminator-Constrained Optimal Transport](https://mlsanity.com/paper/2111.06316/) (2021)
- [On Learning Domain-Invariant Representations for Transfer Learning with Multiple Sources](https://mlsanity.com/paper/2111.13822/) (2021)
- [PAC-Bayesian Domain Adaptation Bounds for Multiclass Learners](https://mlsanity.com/paper/2207.05685/) (2022)
- [Unsupervised Model Adaptation for Source-free Segmentation of Medical Images](https://mlsanity.com/paper/2211.00807/) (2022)
- [Secure Domain Adaptation with Multiple Sources](https://mlsanity.com/paper/2106.12124/) (2021)
- [The Value of Out-of-Distribution Data](https://mlsanity.com/paper/2208.10967/) (2022)
- [Video Unsupervised Domain Adaptation with Deep Learning: A Comprehensive Survey](https://mlsanity.com/paper/2211.10412/) (2022)
- [Multi-Source Domain Adaptation through Dataset Dictionary Learning in Wasserstein Space](https://mlsanity.com/paper/2307.14953/) (2023)
- [Accelerating Sinkhorn Algorithm with Sparse Newton Iterations](https://mlsanity.com/paper/2401.12253/) (2024)
- [Zero-shot Transfer Learning within a Heterogeneous Graph via Knowledge Transfer Networks](https://mlsanity.com/paper/2203.02018/) (2022)
- [Generalizable Domain Adaptation for Sim-and-Real Policy Co-Training](https://mlsanity.com/paper/2509.18631/) (2025)
- [Improving Molecular Representation Learning with Metric Learning-enhanced Optimal Transport](https://mlsanity.com/paper/2202.06208/) (2022)
- [Can Modifying Data Address Graph Domain Adaptation?](https://mlsanity.com/paper/2407.19311/) (2024)
- [Best-Effort Adaptation](https://mlsanity.com/paper/2305.05816/) (2023)
- [Learning Domain Invariant Representations by Joint Wasserstein Distance Minimization](https://mlsanity.com/paper/2106.04923/) (2021)
- [Bridging the Domain Gap for Flight-Ready Spaceborne Vision](https://mlsanity.com/paper/2409.11661/) (2024)
- [Domain Adaptation and Entanglement: an Optimal Transport Perspective](https://mlsanity.com/paper/2503.08155/) (2025)

## Abstract (arXiv)

Domain adaptation (DA) is an important and emerging field of machine learning that tackles the problem occurring when the distributions of training (source domain) and test (target domain) data are similar but different. Current theoretical results show that the efficiency of DA algorithms depends on their capacity of minimizing the divergence between source and target probability distributions. In this paper, we provide a theoretical study on the advantages that concepts borrowed from optimal transportation theory can bring to DA. In particular, we show that the Wasserstein metric can be used as a divergence measure between distributions to obtain generalization guarantees for three different learning settings: (i) classic DA with unsupervised target data (ii) DA combining source and target labeled data, (iii) multiple source DA. Based on the obtained results, we provide some insights showing when this analysis can be tighter than other existing frameworks.