Geometric Structures of Information

Description

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. Front Matter ....Pages i-viii Rho-Tau Embedding of Statistical Models (Jan Naudts, Jun Zhang)....Pages 1-13 A Class of Non-parametric Deformed Exponential Statistical Models (Luigi Montrucchio, Giovanni Pistone)....Pages 15-35 Statistical Manifolds Admitting Torsion and Partially Flat Spaces (Masayuki Henmi, Hiroshi Matsuzoe)....Pages 37-50 Conformal Flattening on the Probability Simplex and Its Applications to Voronoi Partitions and Centroids (Atsumi Ohara)....Pages 51-68 Monte Carlo Information-Geometric Structures (Frank Nielsen, Gaëtan Hadjeres)....Pages 69-103 Information Geometry in Portfolio Theory (Ting-Kam Leonard Wong)....Pages 105-136 Generalising Frailty Assumptions in Survival Analysis: A Geometric Approach (Vahed Maroufy, Paul Marriott)....Pages 137-148 Some Universal Insights on Divergences for Statistics, Machine Learning and Artificial Intelligence (Michel Broniatowski, Wolfgang Stummer)....Pages 149-211 Information-Theoretic Matrix Inequalities and Diffusion Processes on Unimodular Lie Groups (Gregory S. Chirikjian)....Pages 213-249 Warped Riemannian Metrics for Location-Scale Models (Salem Said, Lionel Bombrun, Yannick Berthoumieu)....Pages 251-296 Clustering in Hilbert’s Projective Geometry: The Case Studies of the Probability Simplex and the Elliptope of Correlation Matrices (Frank Nielsen, Ke Sun)....Pages 297-331 Jean-Louis Koszul and the Elementary Structures of Information Geometry (Frédéric Barbaresco)....Pages 333-392