Geometric Structures of Information - Nielsen, Frank; SpringerLink (Online service) (Cham : Springer International Publishing : Imprint: Springer, 2019)
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 attening on the probability simplex and its applications to Voronoi partitions and centroids Atsumi Ohara -- 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 Articial Intelligence -- Information-Theoretic Matrix Inequalities and Diusion Processes on Unimodular Lie Groups.
Keywords: Telecommunication; Coding theory; Information theory; Global analysis (Mathematics).; Manifolds (Mathematics).; Communications Engineering, Networks; Coding and Information Theory; Global Analysis and Analysis on Manifolds