# Partial Distribution Alignment via Adaptive Optimal Transport

arXiv: https://arxiv.org/abs/2503.05087 · HTML: https://mlsanity.com/paper/2503.05087/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 46 references that are in the map.
- First posted on arXiv 7 Mar 2025.

## Builds on (most cited first, 28 of 28)

- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [Deep Transfer Learning with Joint Adaptation Networks](https://mlsanity.com/paper/1605.06636/) (2016)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [VisDA: The Visual Domain Adaptation Challenge](https://mlsanity.com/paper/1710.06924/) (2017)
- [Contrastive Adaptation Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1901.00976/) (2019)
- [A Survey of Unsupervised Deep Domain Adaptation](https://mlsanity.com/paper/1812.02849/) (2018)
- [Joint Distribution Optimal Transportation for Domain Adaptation](https://mlsanity.com/paper/1705.08848/) (2017)
- [DeepJDOT: Deep Joint Distribution Optimal Transport for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1803.10081/) (2018)
- [Mind the Class Weight Bias: Weighted Maximum Mean Discrepancy for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1705.00609/) (2017)
- [Optimal Entropy-Transport problems and a new Hellinger-Kantorovich distance between positive measures](https://mlsanity.com/paper/1508.07941/) (2015)
- [Unbalanced minibatch Optimal Transport; applications to Domain Adaptation](https://mlsanity.com/paper/2103.03606/) (2021)
- [Subspace Robust Wasserstein Distances](https://mlsanity.com/paper/1901.08949/) (2019)
- [Robust Optimal Transport with Applications in Generative Modeling and Domain Adaptation](https://mlsanity.com/paper/2010.05862/) (2020)
- [Deep transfer operator learning for partial differential equations under conditional shift](https://mlsanity.com/paper/2204.09810/) (2022)
- [Adversarial-Learned Loss for Domain Adaptation](https://mlsanity.com/paper/2001.01046/) (2020)
- [Category Contrast for Unsupervised Domain Adaptation in Visual Tasks](https://mlsanity.com/paper/2106.02885/) (2021)
- [Supervised Training of Conditional Monge Maps](https://mlsanity.com/paper/2206.14262/) (2022)
- [Vocabulary Learning via Optimal Transport for Neural Machine Translation](https://mlsanity.com/paper/2012.15671/) (2020)
- [Multilevel Clustering via Wasserstein Means](https://mlsanity.com/paper/1706.03883/) (2017)
- [Outlier-Robust Optimal Transport](https://mlsanity.com/paper/2012.07363/) (2020)
- [Improving Mini-batch Optimal Transport via Partial Transportation](https://mlsanity.com/paper/2108.09645/) (2021)
- [Interpretable bilinear attention network with domain adaptation improves drug-target prediction](https://mlsanity.com/paper/2208.02194/) (2022)
- [On Robust Optimal Transport: Computational Complexity and Barycenter Computation](https://mlsanity.com/paper/2102.06857/) (2021)
- [Outlier-Robust Optimal Transport: Duality, Structure, and Statistical Analysis](https://mlsanity.com/paper/2111.01361/) (2021)
- [Prototypes-oriented Transductive Few-shot Learning with Conditional Transport](https://mlsanity.com/paper/2308.03047/) (2023)

## Abstract (arXiv)

To remedy the drawbacks of full-mass or fixed-mass constraints in classical optimal transport, we propose adaptive optimal transport which is distinctive from the classical optimal transport in its ability of adaptive-mass preserving. It aims to answer the mathematical problem of how to transport the probability mass adaptively between probability distributions, which is a fundamental topic in various areas of artificial intelligence. Adaptive optimal transport is able to transfer mass adaptively in the light of the intrinsic structure of the problem itself. The theoretical results shed light on the adaptive mechanism of mass transportation. Furthermore, we instantiate the adaptive optimal transport in machine learning application to align source and target distributions partially and adaptively by respecting the ubiquity of noises, outliers, and distribution shifts in the data. The experiment results on the domain adaptation benchmarks show that the proposed method significantly outperforms the state-of-the-art algorithms.