On warped product on information geometry: statistical manifolds and statistical models

Fuente: arXiv
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Main Authors: Alba, Nicolás Martínez, Escobar, Olga Garatejo
Format: Preprint
Published: 2024
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author Alba, Nicolás Martínez
Escobar, Olga Garatejo
author_facet Alba, Nicolás Martínez
Escobar, Olga Garatejo
contents We study a differential geometric construction, the warped product, on the background geometry for information theory. Divergences, dual structures and symmetric 3-tensor are studied under this construction, and we show that warped product of manifolds endow with such structure also is endowed with the same geometric notion. However, warped product does not preserve canonical divergences, which in particular shows that warped product lacks of meaning in the information theory setting.
format Preprint
id arxiv_https___arxiv_org_abs_2410_19626
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle On warped product on information geometry: statistical manifolds and statistical models
Alba, Nicolás Martínez
Escobar, Olga Garatejo
Differential Geometry
Information Theory
62B11, 53Z50, 94A15
We study a differential geometric construction, the warped product, on the background geometry for information theory. Divergences, dual structures and symmetric 3-tensor are studied under this construction, and we show that warped product of manifolds endow with such structure also is endowed with the same geometric notion. However, warped product does not preserve canonical divergences, which in particular shows that warped product lacks of meaning in the information theory setting.
title On warped product on information geometry: statistical manifolds and statistical models
topic Differential Geometry
Information Theory
62B11, 53Z50, 94A15
url https://arxiv.org/abs/2410.19626