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 …

Abstract Information geometry and optimal transport are two distinct geometric frameworks
for modeling families of probability measures. During the recent years, there has been a …

This paper systematically presents the λ-deformation as the canonical framework of
deformation to the dually flat (Hessian) geometry, which has been well established in …

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

In this article, we consider statistical submanifolds of Kenmotsu statistical manifolds of
constant ϕ-sectional curvature. For such submanifold, we investigate curvature properties …

We study Codazzi couplings of an affine connection ∇∇ with a pseudo-Riemannian metric
g, a nondegenerate 2-form ω ω, and a tangent bundle isomorphism L on smooth manifolds …

We describe a framework to build distances by measuring the tightness of inequalities and
introduce the notion of proper statistical divergences and improper pseudo-divergences. We …

Abstract Markov chain Monte Carlo methods for sampling from complex distributions and
estimating normalization constants often simulate samples from a sequence of intermediate …

Comparative convexity is a generalization of ordinary convexity based on abstract means
instead of arithmetic means. We introduce the generalized skew Jensen divergences and …

The standard model of information geometry, expressed as Fisher–Rao metric and Amari-
Chensov tensor, reflects an embedding of probability density by\log log-transform. The …