Abstract
We study the sample complexity of entropic optimal transport in high dimensions using computationally efficient plug-in estimators. We significantly advance the state of the art by establishing dimension-free, parametric rates for estimating various quantities of interest, including the entropic regression function, which is a natural analog to the optimal transport map. As an application, we propose a practical model for transfer learning based on entropic optimal transport and establish parametric rates of convergence for nonparametric regression and classification.
| Original language | English |
|---|---|
| Pages (from-to) | 61-90 |
| Number of pages | 30 |
| Journal | Annals of Statistics |
| Volume | 53 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Feb 2025 |
| Externally published | Yes |
Keywords
- Optimal transport
- Schrödinger bridge
- entropic regularization
- statistical rates