A metric structure of statistical manifolds based on optimal transportation theory
Chunyan Zhao, Yu‐Jie Huang, Qin Zhong, Mei Zhang · 2023
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.