Wasserstein Riemannian Geometry on Statistical Manifold

Year 2020, , 144 - 151, 15.10.2020

Carlos Ogouyandjou , Nestor Wadagnı

https://doi.org/10.36890/iejg.689702

Abstract

In this paper, we study some geometric properties of statistical manifold equipped with the Riemannian Otto metric which is related to the L 2 -Wasserstein distance of optimal mass transport. We construct some α -connections on such manifold and we prove that the proposed connections are torsion-free and coincide with the Levi-Civita connection when α = 0 . In addition, the exponentialy families and the mixture families are shown to be respectively (1) -flat and (−1) -flat.                                                                                                                                             ..............................................

Keywords

Statistical manifold, Riemannian metric, Otto metric, α-connections, Wasserstein Riemannian space, flatness

Supporting Institution

CEA-SMA (IMSP) University of Abomey-Calavi, Benin

Thanks

The authors would like to thank the CEA-SMA (IMSP) University of Abomey-Calavi, Benin for their support.

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