2022/04/02 by Goffredo Chirco, Chirco, Goffredo, Giovanni Pistone +1
Computer Science · #FOS: Mathematics #Rough Sets and Fuzzy Logic #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2204.00917
openalex publication_date 2022/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.