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arXiv · 2204.00917

Dually affine Information Geometry modeled on a Banach space

Goffredo Chirco·Giovanni Pistone
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Abstract

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.

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Goffredo Chirco, Giovanni Pistone. 2022-04-02. Dually affine Information Geometry modeled on a Banach space. https://arxiv.org/abs/2204.00917

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