viii
Preface
Preparing this edited book during the pandemic was a different experience than in
normal times: We had to allocate extra time for some contributors and reviewers, and
to take into account personal situations to adapt the project. We are very grateful to the
contributors and reviewers for their devoted times and efforts during this exceptional
period, where most colleagues have to work remotely from home and had to quickly
adapt to the evolving situation.
This edited book is organized into ten chapters, which are organized into two
parts as follows: The first part deals with recent advances on the fundamentals of
information geometry and the second part explores connections or potential
interactions of information geometry with other domains (e.g., time-series analysis
or optimal transport).
The first part on the fundamentals of information geometry is structured as follows:
• Professor Pistone further explores non-parametric information geometry in the
chapter entitled “Information Geometry of Smooth Densities on the Gaussian
Space: Poincaré Inequalities”.
• Professors de Andrade, Vieira, and Cavalcante report the latest results in
deformed exponential families in the chapter entitled “On Normalization
Functions and ϕ-Families of Probability Distributions”.
• Professors Zhang and Khan investigate affine connections with torsions in the
chapter entitled “Affine Connections with Torsion in (Para-)complexified
Structures”.
• Professors Goto and Hino study the master equations and expectation variables
of the moment dynamical system derived from the master equations using paracontact metric manifolds in the chapter entitled “Contact Hamiltonian Systems
for Probability Distribution Functions and Expectation Variables: A Study Based
on a Class of Master Equations”.
• Professor Barbaresco considers homogeneous bounded domains and invariant
Koszul form and its relationship with information geometry in the chapter entitled
“Invariant Koszul Form of Homogeneous Bounded Domains and Information
Geometry Structures”.
• Professors Matsuzoe and Takatsu study gauge freedom in the chapter entitled
“Gauge Freedom of Entropies on q-Gaussian Measures”.
• Professor Nielsen investigates right-angles in (possibly mixed) geodesic triangles
in dually flat spaces in the chapter entitled “On Geodesic Triangles with Right
Angles in a Dually Flat Space”.
The second part on connections or possible interactions of information geometry
with other areas is structured as follows:
• Professors Nielsen and Sun introduce a novel metric distance based on optimal
transport in the chapter entitled “Chain Rule Optimal Transport”.
• Professors Cole and Shiu present some work on Topological Data Analysis (TDA)
in theoretical physics in the chapter entitled “Towards the “Shape” of Cosmological
Observables and the String Theory Landscape with Topological Data Analysis”.
Preface
Preparing this edited book during the pandemic was a different experience than in
normal times: We had to allocate extra time for some contributors and reviewers, and
to take into account personal situations to adapt the project. We are very grateful to the
contributors and reviewers for their devoted times and efforts during this exceptional
period, where most colleagues have to work remotely from home and had to quickly
adapt to the evolving situation.
This edited book is organized into ten chapters, which are organized into two
parts as follows: The first part deals with recent advances on the fundamentals of
information geometry and the second part explores connections or potential
interactions of information geometry with other domains (e.g., time-series analysis
or optimal transport).
The first part on the fundamentals of information geometry is structured as follows:
• Professor Pistone further explores non-parametric information geometry in the
chapter entitled “Information Geometry of Smooth Densities on the Gaussian
Space: Poincaré Inequalities”.
• Professors de Andrade, Vieira, and Cavalcante report the latest results in
deformed exponential families in the chapter entitled “On Normalization
Functions and ϕ-Families of Probability Distributions”.
• Professors Zhang and Khan investigate affine connections with torsions in the
chapter entitled “Affine Connections with Torsion in (Para-)complexified
Structures”.
• Professors Goto and Hino study the master equations and expectation variables
of the moment dynamical system derived from the master equations using paracontact metric manifolds in the chapter entitled “Contact Hamiltonian Systems
for Probability Distribution Functions and Expectation Variables: A Study Based
on a Class of Master Equations”.
• Professor Barbaresco considers homogeneous bounded domains and invariant
Koszul form and its relationship with information geometry in the chapter entitled
“Invariant Koszul Form of Homogeneous Bounded Domains and Information
Geometry Structures”.
• Professors Matsuzoe and Takatsu study gauge freedom in the chapter entitled
“Gauge Freedom of Entropies on q-Gaussian Measures”.
• Professor Nielsen investigates right-angles in (possibly mixed) geodesic triangles
in dually flat spaces in the chapter entitled “On Geodesic Triangles with Right
Angles in a Dually Flat Space”.
The second part on connections or possible interactions of information geometry
with other areas is structured as follows:
• Professors Nielsen and Sun introduce a novel metric distance based on optimal
transport in the chapter entitled “Chain Rule Optimal Transport”.
• Professors Cole and Shiu present some work on Topological Data Analysis (TDA)
in theoretical physics in the chapter entitled “Towards the “Shape” of Cosmological
Observables and the String Theory Landscape with Topological Data Analysis”.