A characterization of the alpha-connections on the statistical manifold of normal distributions

2020/05/28 by Hitoshi Furuhata, Furuhata, Hitoshi, Jun-ichi Inoguchı +3 · 2 citations
Computer Science · Mathematics · #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Primary 53A15 #Secondary 22E25 #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2005.13927

openalex publication_date 2020/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the statistical manifold of normal distributions is homogeneous. In particular, it admits a 2-dimensional solvable Lie group structure. In addition, we give a geometric characterization of the Amari-Chentsov α-connections on the Lie group.

Citations

• Invariant Affine Connections on Homogeneous Spaces

Cited by

• The moduli spaces of left-invariant statistical structures on Lie groups
• The Second Variational Formula for Statistical Biharmonic Maps

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