Geometric Structures of Information [electronic resource] /
edited by Frank Nielsen.
- 1st ed. 2019.
- VIII, 392 p. 49 illus., 36 illus. in color. online resource.
- Signals and Communication Technology, 1860-4870 .
- Signals and Communication Technology, .
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.
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.
9783030025205
10.1007/978-3-030-02520-5 doi
Telecommunication.
Coding theory.
Information theory.
Global analysis (Mathematics).
Manifolds (Mathematics).
Communications Engineering, Networks.
Coding and Information Theory.
Global Analysis and Analysis on Manifolds.
TK5101-5105.9
621.382
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.
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.
9783030025205
10.1007/978-3-030-02520-5 doi
Telecommunication.
Coding theory.
Information theory.
Global analysis (Mathematics).
Manifolds (Mathematics).
Communications Engineering, Networks.
Coding and Information Theory.
Global Analysis and Analysis on Manifolds.
TK5101-5105.9
621.382