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Fisher-Rao geometry of Dirichlet distributions

Abstract : 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 geodesically complete and has everywhere negative sectional curvature. An important consequence of this negative curvature for applications is that the Fréchet mean of a set of Dirichlet distributions is uniquely defined in this geometry.
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https://hal.archives-ouvertes.fr/hal-02568473
Contributor : Alice Le Brigant <>
Submitted on : Saturday, May 9, 2020 - 1:01:54 PM
Last modification on : Monday, June 29, 2020 - 3:11:31 AM

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  • HAL Id : hal-02568473, version 1
  • ARXIV : 2005.05608

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Alice Le Brigant, Stephen Preston, Stéphane Puechmorel. Fisher-Rao geometry of Dirichlet distributions. 2020. ⟨hal-02568473⟩

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