Overview

Information geometry provides the mathematical sciences with a new framework of analysis. It has emerged from the investigation of the natural differential geometric structure on manifolds of probability distributions, which consists of a Riemannian metric defined by the Fisher information and a one-parameter family of affine connections called the $\alpha$-connections. The duality between the $\alpha$-connection and the $(-\alpha)$-connection together with the metric play an essential role in this geometry. This kind of duality, having emerged from manifolds of probability distributions, is ubiquitous, appearing in a variety of problems which might have no explicit relation to probability theory. Through the duality, it is possible to analyze various fundamental problems in a unified perspective. The first half of this book is devoted to a comprehensive introduction to the mathematical foundation of information geometry, including preliminaries from differential geometry, the geometry of manifolds or probability distributions, and the general theory of dual affine connections.The second half of the text provides an overview of many areas of applications, such as statistics, linear systems, information theory, quantum mechanics, convex analysis, neural networks, and affine differential geometry. The book can serve as a suitable text for a topics course for advanced undergraduates and graduate students.

Full Product Details

9780821843024

Table of Contents

Reviews

Presents for the first time the entirety of the emerging field of information geometry ... this book will play a key role for the further progress of information geometry. - Zentralblatt MATH Until now there have been no expository textbooks covering the methods and applications of information geometry. The present monograph will be extremely useful in dissemination of knowledge in this area and promoting much-needed research ...This monograph is a welcome and much-needed addition to the literature on the use of differential geometry methods in statistics, information theory and control theory. Research workers in statistics and information theory will greatly benefit by studying the concepts and methods discussed in the monograph. - Mathematical Reviews

Author Information

Shun-ichi Amari, RIKEN Brain Science Institute, Saitama, Japan Hiroshi Nagaoka, University of Electro-Communications, Tokyo, Japan

Tab Content 6

Customer Reviews

Recent Reviews

Countries Available