In this survey, we describe the fundamental differential-geometric structures of information
manifolds, state the fundamental theorem of information geometry, and illustrate some use …

The Wasserstein distance on multivariate non-degenerate Gaussian densities is a
Riemannian distance. After reviewing the properties of the distance and the metric geodesic …

In the framework of quantum information geometry, we derive, from quantum relative Tsallis
entropy, a family of quantum metrics on the space of full rank, N level quantum states, by …

Tsallis and Rényi entropies, which are monotone transformations of each other, are
deformations of the celebrated Shannon entropy. Maximization of these deformed entropies …

This paper reviews the role of convex duality in Information Geometry. It clarifies the notion
of bi-orthogonal coordinates associated with Legendre duality by treating its two underlying …

We illustrate some financial applications of the Tsallis and Kaniadakis deformed
exponential. The minimization of the corresponding deformed divergence is discussed as a …

We provide an Information-Geometric formulation of accelerated natural gradient on the
Riemannian manifold of probability distributions, which is an affine manifold endowed with a …

This chapter represents the most important technical achievement of this book, a
combination of functional analysis and geometry as the natural framework for families of …

We review a nonparametric version of Amari's information geometry in which the set of
positive probability densities on a given sample space is endowed with an atlas of charts to …

Information geometry is a study of statistical manifolds, that is, spaces of probability
distributions from a geometric perspective. Its classical information-theoretic applications …