Springer, 2019. — 395 p. — (Signals and Communication Technology). — ISBN: 3030025195.
This book focuses on information geometry manifolds of structured data/information and their advanced applications featuring new and fruitful interactions between several branches of science: information science, mathematics and physics. It addresses interrelations between different mathematical domains like shape spaces, probability/optimization & algorithms on manifolds, relational and discrete metric spaces, computational and Hessian information geometry, algebraic/infinite dimensional/Banach information manifolds, divergence geometry, tensor-valued morphology, optimal transport theory, manifold & topology learning, and applications like geometries of audio-processing, inverse problems and signal processing. The book collects the most important contributions to the conference GSI'2017 - Geometric Science of Information.
Rho-Tau Embedding of Statistical Models
A Class of Non-parametric Deformed Exponential Statistical Models
Statistical Manifolds Admitting Torsion and Partially Flat Spaces
Conformal Flattening on the Probability Simplex and Its Applications to Voronoi Partitions and Centroids
Monte Carlo Information-Geometric Structures
Information Geometry in Portfolio Theory
Generalising Frailty Assumptions in Survival Analysis: A Geometric Approach
Some Universal Insights on Divergences for Statistics, Machine Learning and Artificial Intelligence
Information-Theoretic Matrix Inequalities and Diffusion Processes on Unimodular Lie Groups
Warped Riemannian Metrics for Location-Scale Models
Clustering in Hilbert’s Projective Geometry: The Case Studies of the Probability Simplex and the Elliptope of Correlation Matrices
Jean-Louis Koszul and the Elementary Structures of Information Geometry