论文标题
当最佳运输符合信息几何形状时
When Optimal Transport Meets Information Geometry
论文作者
论文摘要
信息几何和最佳传输是两个不同的几何框架，用于建模概率度量的家族。近年来，研究努力席卷了这两个领域，并探索了它们的联系和互动。本文旨在对这些作品提供（不完整的）调查，包括熵登记的运输，$ C $双重性，密度歧管和传输信息几何形状，Para-Kähler和Kähller几何形状产生的差异功能以及其解决方案的正常运输理论。提出了这两个学科的观众感兴趣的一些杰出问题。我们的文章还可以介绍有关期刊信息几何形状的最佳运输特刊。
Information geometry and optimal transport are two distinct geometric frameworks for modeling families of probability measures. During the recent years, there has been a surge of research endeavors that cut across these two areas and explore their links and interactions. This paper is intended to provide an (incomplete) survey of these works, including entropy-regularized transport, divergence functions arising from $c$-duality, density manifolds and transport information geometry, the para-Kähler and Kähler geometries underlying optimal transport and the regularity theory for its solutions. Some outstanding questions that would be of interest to audience of both these two disciplines are posed. Our piece also serves as an introduction to the Special Issue on Optimal Transport of the journal Information Geometry.
