Fisher-Rao geometry of Dirichlet distributions

被引：11

作者：

Brigant, Alice Le ^{[1
]}

Preston, Stephen C. ^{[2
,3
]}

Puechmorel, Stephane ^{[4
]}

机构：

[1] Univ Paris 1 Pantheon Sorbonne, Ctr PMF, SAMM 4543, Paris, France

[2] Brooklyn Coll, Dept Math, New York, NY USA

[3] CUNY, Grad Ctr, New York, NY USA

[4] Univ Toulouse, Ecole Natl Aviat Civile, Toulouse, France

来源：

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2021年 / 74卷

关键词：

D O I：

10.1016/j.difgeo.2020.101702

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the geometry induced by the Fisher-Rao metric on the parameter space of Dirichlet distributions. We show that this space is a Hadamard manifold, i.e. that it is geodesically complete and has everywhere negative sectional curvature. An important consequence for applications is that the Frechet mean of a set of Dirichlet distributions is uniquely defined in this geometry. (C) 2020 Elsevier B.V. All rights reserved.

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页数：16

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