Dually affine Information Geometry modeled on a Banach space
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.
Keywords
Cite
@article{arxiv.2204.00917,
title = {Dually affine Information Geometry modeled on a Banach space},
author = {Goffredo Chirco and Giovanni Pistone},
journal= {arXiv preprint arXiv:2204.00917},
year = {2024}
}
Comments
Submitted as a contributed chapter in a collective handbook. Added a section on the geometry of the unit sphere