A metric structure of statistical manifolds based on optimal transportation theory

Chunyan Zhao; Yujie Huang; Qin Zhong; Mei Zhang

doi:10.1117/12.2679132

14 June 2023 A metric structure of statistical manifolds based on optimal transportation theory

Chunyan Zhao, Yujie Huang, Qin Zhong, Mei Zhang

Proceedings Volume 12725, International Conference on Pure, Applied, and Computational Mathematics (PACM 2023); 127250B (2023) https://doi.org/10.1117/12.2679132
Event: International Conference on Pure, Applied, and Computational Mathematics (PACM 2023), 2023, Suzhou, China

Abstract

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.

Citation Download Citation

Chunyan Zhao, Yujie Huang, Qin Zhong, and Mei Zhang "A metric structure of statistical manifolds based on optimal transportation theory", Proc. SPIE 12725, International Conference on Pure, Applied, and Computational Mathematics (PACM 2023), 127250B (14 June 2023); https://doi.org/10.1117/12.2679132

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