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Dergiler / International Electronic Journal of Geometry / 2020 / Volume: 13 Issue: 2

Wasserstein Riemannian Geometry on Statistical Manifold

Carlos Ogouyandjou(Université d'Abomey-Calavi (UAC), Institut de Mathématiques et de Sciences Physiques (IMSP))0000-0001-7115-7724
Nestor Wadagnı(Institut de Mathématiques et de Sciences Physiques(IMSP), Université d’Abomey-Calavi(UAC), Bénin)0000-0001-8757-176X
Sayfa
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Yayın Tarihi
2020-10-15
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In addition, the exponentialy families and the mixture families are shown to be respectively (1) -flat and (−1) -flat. ..............................................

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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.
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Temel Bulgular & Veri: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 .
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Sonuç & Katkı:In addition, the exponentialy families and the mixture families are shown to be respectively (1) -flat and (−1) -flat. ..............................................
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Statistical manifold · Riemannian metric · Otto metric

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. ..............................................

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Bu Makaleye Atıf Yap

Ogouyandjou, C., Wadagnı, N. (2020). Wasserstein Riemannian Geometry on Statistical Manifold. International Electronic Journal of Geometry, Volume: 13 Issue: 2. https://doi.org/10.36890/iejg.689702

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Kaynakça (11)

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