Learning Representations That Are Closed-Form Monge Mapping Optimal with Application to Domain Adaptation
Abstract
Optimal transport (OT) is a powerful geometric tool used to compare and align probability measures following the least effort principle. Despite its widespread use in machine learning (ML), OT problem still bears its computational burden, while at the same time suffering from the curse of dimensionality for measures supported on general high-dimensional spaces. In this paper, we propose to tackle these challenges using representation learning. In particular, we seek to learn an embedding space such that the samples of the two input measures become alignable in it with a simple affine mapping that can be calculated efficiently in closed-form. We then show that such approach leads to results that are comparable to solving the original OT problem when applied to the transfer learning task on which many OT baselines where previously evaluated in both homogeneous and heterogeneous DA settings.
Cite
Text
Struckmeier et al. "Learning Representations That Are Closed-Form Monge Mapping Optimal with Application to Domain Adaptation." Transactions on Machine Learning Research, 2023.Markdown
[Struckmeier et al. "Learning Representations That Are Closed-Form Monge Mapping Optimal with Application to Domain Adaptation." Transactions on Machine Learning Research, 2023.](https://mlanthology.org/tmlr/2023/struckmeier2023tmlr-learning/)BibTeX
@article{struckmeier2023tmlr-learning,
title = {{Learning Representations That Are Closed-Form Monge Mapping Optimal with Application to Domain Adaptation}},
author = {Struckmeier, Oliver and Redko, Ievgen and Mallasto, Anton and Arndt, Karol and Heinonen, Markus and Kyrki, Ville},
journal = {Transactions on Machine Learning Research},
year = {2023},
url = {https://mlanthology.org/tmlr/2023/struckmeier2023tmlr-learning/}
}