2024
DOI: 10.1007/s41884-024-00139-y
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Information geometry of Wasserstein statistics on shapes and affine deformations

Shun-ichi Amari,
Takeru Matsuda

Abstract: Information geometry and Wasserstein geometry are two main structures introduced in a manifold of probability distributions, and they capture its different characteristics. We study characteristics of Wasserstein geometry in the framework of [32] for the affine deformation statistical model, which is a multi-dimensional generalization of the location-scale model. We compare merits and demerits of estimators based on information geometry and Wasserstein geometry. The shape of a probability distribution and its … Show more

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