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 …

This work gives an overview of statistical analysis for some models for multivariate discrete-
valued (MDV) time series. We present observation-driven models and models based on …

Information geometry and Markov chains are two powerful tools used in modern fields such
as finance, physics, computer science, and epidemiology. In this survey, we explore their …

We formulate em algorithm in the framework of Bregman divergence, which is a general
problem setting of information geometry. That is, we address the minimization problem of the …

We introduce a new information-geometric structure associated with the dynamics on
discrete objects such as graphs and hypergraphs. The presented setup consists of two …

We analyze the information geometric structure of time reversibility for parametric families of
irreducible transition kernels of Markov chains. We define and characterize reversible …

The spectral gap ⋆ of a finite, ergodic and reversible Markov chain is an important
parameter measuring the asymptotic rate of convergence. In applications, the transition …

Using terminologies of information geometry, we derive upper and lower bounds of the tail
probability of the sample mean for the Markov chain with finite state space. Employing these …

In this paper, we derive non-asymptotic achievability and converse bounds on the random
number generation with/without side-information. Our bounds are efficiently computable in …