On information geometry methods for data analysis

Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F24%3A73626814" target="_blank" >RIV/61989592:15310/24:73626814 - isvavai.cz</a>
Výsledek na webu
<a href="https://www.researchgate.net/publication/385837561_On_Information_Geometry_Methods_for_Data_Analysis" target="_blank" >https://www.researchgate.net/publication/385837561_On_Information_Geometry_Methods_for_Data_Analysis</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.7546/giq-29-2024-11-22" target="_blank" >10.7546/giq-29-2024-11-22</a>

Jazyk výsledku
angličtina
Název v původním jazyce
On information geometry methods for data analysis
Popis výsledku v původním jazyce
The paper is devoted to exploration of statistical manifolds. In particular we consider exponential family manifolds, its metrics and connections. We proved that a statistical manifold does not admit nontrivial geodesic mapping between the Riemannian connection and any alpha-connection. Besides, a statistical manifold does not admit a Weyl connection which coincides with any alpha-connection. We obtain also that the Fisher information matrix calculated for a mixture family is a Hessian metric.
Název v anglickém jazyce
On information geometry methods for data analysis
Popis výsledku anglicky
The paper is devoted to exploration of statistical manifolds. In particular we consider exponential family manifolds, its metrics and connections. We proved that a statistical manifold does not admit nontrivial geodesic mapping between the Riemannian connection and any alpha-connection. Besides, a statistical manifold does not admit a Weyl connection which coincides with any alpha-connection. We obtain also that the Fisher information matrix calculated for a mixture family is a Hessian metric.

Rok uplatnění
2024
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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