On warped product on information geometry: statistical manifolds and statistical models
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910667501469696 |
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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 |
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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 |