基于最优运输理论的统计流形度量结构

Conference on Pure, Applied, and Computational Mathematics Pub Date : 2023-06-14 DOI:10.1117/12.2679132

Chunyan Zhao, Yujie Huang, Qin Zhong, Mei Zhang

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引用次数: 0

摘要

最优传输中的沃瑟斯坦距离提供了一个数学工具来测量函数或更一般的对象之间的距离。利用Wasserstein距离，定义了一类统计流形模空间上的距离。我们构造了这个空间的黎曼度规，并验证了定义的距离可以看作是这个度规的诱导距离。

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A metric structure of statistical manifolds based on optimal transportation theory

Wasserstein distances in optimal transport provides a mathematical tool to measure distances between functions or more general objects. By Wasserstein distances, we define a distance on the moduli space of a class of statistical manifolds. We construct a Riemannian metric of this space and verify that the defined distance can be regarded as the induced distance of the metric.

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Conference on Pure, Applied, and Computational Mathematics

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