为最优传输映射提供统计推断工具，助力可靠分析
Statistical Inference for Optimal Transport Maps: Recent Advances and Perspectives
- 基于样本数据估计最优传输映射的分布特性
- 建立映射估计量的渐近正态性与极限定理
- 适合需要量化不确定性的机器学习与统计应用
在最优传输（OT）的诸多应用中，核心关注对象是最优传输映射。该映射通过最小化指定代价函数，以最高效的方式将一个概率分布的质量重新分配至另一个分布。本文综述了近期关于从底层分布样本中估计最优传输映射并建立其极限定理的研究进展，同时回顾了基本OT框架特殊情形与变体的类似成果。最后，文章讨论了未来研究的关键方向，旨在为实践者提供可靠的统计推断工具。
原文摘要 · Abstract (English)
In many applications of optimal transport (OT), the object of primary interest is the optimal transport map. This map rearranges mass from one probability distribution to another in the most efficient way possible by minimizing a specified cost. In this paper we review recent advances in estimating and developing limit theorems for the OT map, using samples from the underlying distributions. We also review parallel lines of work that establish similar results for special cases and variants of the basic OT setup. We conclude with a discussion of key directions for future research with the goal of providing practitioners with reliable inferential tools.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。