Geometric Structures of Information

著者名：Nielsen, Frank (EDT)

Springer（2018/11/19発売）

• 言語：ENG
• ISBN：9783030025199
• eISBN：9783030025205

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.

Table of Contents

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.