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Dergiler / International Electronic Journal of Geometry / 2020 / Cilt: 13 - Sayı: 2

Wasserstein Riemannian Geometry on Statistical Manifold

Carlos OGOUYANDJOU
Nestor WADAGNI
Sayfa
144–151
Yayın Tarihi
2022-10-18
DOI
—
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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:Araştırma Makalesi
📍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., WADAGNI, N. (2022). Wasserstein Riemannian Geometry on Statistical Manifold. International Electronic Journal of Geometry, Cilt: 13 - Sayı: 2, 144–151. https://ajindex.com/articles/539617

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Kaynakça (10)

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