TY  - JOUR
T1  - Wasserstein Riemannian Geometry on Statistical Manifold
AU  - Ogouyandjou, Carlos
AU  - Wadagnı, Nestor
PY  - 2020
DA  - October
Y2  - 2020
DO  - 10.36890/iejg.689702
JF  - International Electronic Journal of Geometry
JO  - Int. Electron. J. Geom.
PB  - Kazım İlarslan
WT  - DergiPark
SN  - 1307-5624
SP  - 144
EP  - 151
VL  - 13
IS  - 2
LA  - en
AB  - 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.                                                                      ..............................................
KW  - Statistical manifold
KW  - Riemannian metric
KW  - Otto metric
KW  - α-connections
KW  - Wasserstein Riemannian space
KW  - flatness
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UR  - https://doi.org/10.36890/iejg.689702
L1  - https://dergipark.org.tr/en/download/article-file/970344
ER  -