Information geometry is the differential geometric treatment of statistical models. It thereby
provides the mathematical foundation of statistics. Information geometry therefore is of …

This is the first comprehensive book on information geometry, written by the founder of the
field. It begins with an elementary introduction to dualistic geometry and proceeds to a wide …

An exponential family or mixture family of probability distributions has a natural hierarchical
structure. This paper gives an" orthogonal" decomposition of such a system based on …

Indeed, information geometry, IG is an ever-growing area with a great scope of applications
ranging from Probability & Statistics, Machine Learning (ML), Artificial Intelligence (AI) …

Differential geometry provides an aesthetically appealing and oftenrevealing view of
statistical inference. Beginning with anelementary treatment of one-parameter statistical …

Measures of divergence between two points play a key role in many engineering problems.
One such measure is a distance function, but there are many important measures which do …

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

We review the introduction of several types of projection filters. Projection structures coming
from information geometry are used to obtain a finite dimensional filter in the form of a …

In this paper, we consider an infinite dimensional exponential family P of probability
densities, which are parametrized by functions in a reproducing kernel Hilbert space H, and …

Abstract Information geometry provides a geometric approach to families of statistical
models. The key geometric structures are the Fisher quadratic form and the Amari–Chentsov …