ON THE SAMPLE COMPLEXITY OF ENTROPIC OPTIMAL TRANSPORT

• 成果类型: Article
• 署名作者: Igollet, Philippe; Tromme, Austin j.
• 署名单位: Massachusetts Institute of Technology (MIT); Institut Polytechnique de Paris; ENSAE Paris
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/24-AOS2455
• 发表日期: 2025
• 页码: 61-90
• 关键词: regularized optimal transport; convergence-rates; LIMIT-THEOREMS; asymptotics; MAPS

摘要

We study the sample complexity of entropic optimal transport in high diadvance 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.