Simplifying Optimal Transport through Schatten-$p$ Regularization
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908591162654720 |
|---|---|
| author | Maunu, Tyler |
| author_facet | Maunu, Tyler |
| contents | We propose a new general framework for recovering low-rank structure in optimal transport using Schatten-$p$ norm regularization. Our approach extends existing methods that promote sparse and interpretable transport maps or plans, while providing a unified and principled family of convex programs that encourage low-dimensional structure. The convexity of our formulation enables direct theoretical analysis: we derive optimality conditions and prove recovery guarantees for low-rank couplings and barycentric maps in simplified settings. To efficiently solve the proposed program, we develop a mirror descent algorithm with convergence guarantees for $p \geq 1$. Experiments on synthetic and real data demonstrate the method's efficiency, scalability, and ability to recover low-rank transport structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11910 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simplifying Optimal Transport through Schatten-$p$ Regularization Maunu, Tyler Machine Learning We propose a new general framework for recovering low-rank structure in optimal transport using Schatten-$p$ norm regularization. Our approach extends existing methods that promote sparse and interpretable transport maps or plans, while providing a unified and principled family of convex programs that encourage low-dimensional structure. The convexity of our formulation enables direct theoretical analysis: we derive optimality conditions and prove recovery guarantees for low-rank couplings and barycentric maps in simplified settings. To efficiently solve the proposed program, we develop a mirror descent algorithm with convergence guarantees for $p \geq 1$. Experiments on synthetic and real data demonstrate the method's efficiency, scalability, and ability to recover low-rank transport structures. |
| title | Simplifying Optimal Transport through Schatten-$p$ Regularization |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2510.11910 |