Reprint

# Information Geometry

Edited by

April 2019

356 pages

- ISBN978-3-03897-632-5 (Paperback)
- ISBN978-3-03897-633-2 (PDF)

This is a Reprint of the Special Issue Information Geometry that was published in

Chemistry & Materials Science

Computer Science & Mathematics

Physical Sciences

Summary

This Special Issue of the journal Entropy, titled “Information Geometry I”, contains a collection of 17 papers concerning the foundations and applications of information geometry. Based on a geometrical interpretation of probability, information geometry has become a rich mathematical field employing the methods of differential geometry. It has numerous applications to data science, physics, and neuroscience. Presenting original research, yet written in an accessible, tutorial style, this collection of papers will be useful for scientists who are new to the field, while providing an excellent reference for the more experienced researcher. Several papers are written by authorities in the field, and topics cover the foundations of information geometry, as well as applications to statistics, Bayesian inference, machine learning, complex systems, physics, and neuroscience.

Format

- Paperback

License and Copyright

© 2019 by the authors; CC BY-NC-ND license

Keywords

Markov random fields; information theory; Fisher information; entropy; maximum pseudo-likelihood estimation; Bezout matrix; Sylvester matrix; tensor Sylvester matrix; Stein equation; Vandermonde matrix; stationary process; matrix resultant; Fisher information matrix; information geometry; dually flat structure; decomposable divergence; (ρ,τ) -structure; information geometry; computational geometry; statistical foundations; embedding; Amari’s

*α*-connections;*F*-metric;*F*-connections; (*F,G*)-metric; (*F,G*)-connections; invariance; probability theory; Riemannian geometry; complexity; Bayesian prediction; Fisher information; Kullback–Leibler divergence; minimax; predictive metric; subminimax estimator; information geometry; Markov chain Monte Carlo; Bayesian inference; computational statistics; machine learning; statistical mechanics; diffusions; Fisher information metric; information geometry; convex support polytope; conditional model; Markov morphism; isometric embedding; natural gradient; bag-of-X; α-divergence; Jeffreys divergence; centroid; k-means clustering; k-means seeding; information geometry; Boltzmann machine; Fisher information; parametric reduction; information geometry; variational Bayes; regime-switching log-normal model; model selection; covariance estimation; quantum entropy; metric; q-bit; information; geometry; geodesics; relevant entropy; Fisher information; Riemannian metric; prior distribution; univariate normal distribution; image classification; simplex; cone; exponential family; monotone likelihood ratio; unimodal; duality; information geometry; complexity measure; complex network; system decompositionability; geometric mean; statistical manifold; Riemannian Hessian; combinatorial optimization; Newton method