Dually affine Information Geometry modeled on a Banach space
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866909198352121856 |
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| author | Chirco, Goffredo Pistone, Giovanni |
| author_facet | Chirco, Goffredo Pistone, Giovanni |
| contents | In this chapter, we study Information Geometry from a particular non-parametric or functional point of view. The basic model is a probabilities subset usually specified by regularity conditions. For example, probability measures mutually absolutely continuous or probability densities with a given degree of smoothness. We construct a manifold structure by giving an atlas of charts as mappings from probabilities to a Banach space. The charts we use are quite peculiar in that we consider only instances where the transition mappings are affine. We chose a particular expression of the tangent and cotangent bundles in this affine setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_00917 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Dually affine Information Geometry modeled on a Banach space Chirco, Goffredo Pistone, Giovanni Statistics Theory In this chapter, we study Information Geometry from a particular non-parametric or functional point of view. The basic model is a probabilities subset usually specified by regularity conditions. For example, probability measures mutually absolutely continuous or probability densities with a given degree of smoothness. We construct a manifold structure by giving an atlas of charts as mappings from probabilities to a Banach space. The charts we use are quite peculiar in that we consider only instances where the transition mappings are affine. We chose a particular expression of the tangent and cotangent bundles in this affine setting. |
| title | Dually affine Information Geometry modeled on a Banach space |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2204.00917 |