- International Electronic Journal of Geometry
- Vol: 13 Issue: 2
- Wasserstein Riemannian Geometry on Statistical Manifold
Wasserstein Riemannian Geometry on Statistical Manifold
Authors : Carlos Ogouyandjou, Nestor Wadagni
Pages : 144-151
Doi:10.36890/iejg.689702
View : 7 | Download : 5
Publication Date : 2020-10-15
Article Type : Research
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