Infinite-Dimensional Statistical Manifolds based on a Balanced Chart

Abstract

We develop a family of infinite-dimensional Banach manifolds of measures on an abstract measurable space, employing charts that are “balanced” between the density and log-density functions. The manifolds, (M̃λ, λ ∈ [2,∞)), retain many of the features of finite-dimensional information geometry; in particular, the α-divergences are of class Cdλe−1, enabling… (More)

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