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Methods of Information Geometry
Shun-Ichi Amari (Ed.)
€ 167.77
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Description for Methods of Information Geometry
Paperback. Information geometry provides the mathematical sciences with a fresh framework of analysis. This book presents a comprehensive introduction to the mathematical foundation of information geometry. It provides an overview of many areas of applications, such as statistics, linear systems, information theory, quantum mechanics, and convex analysis. Editor(s): Amari, Shun-ichi; Nagaoka, Hiroshi. Series: Translations of Mathematical Monographs Reprint. Num Pages: 206 pages. BIC Classification: PBMP; PBT; UYA; UYD. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 260 x 180 x 15. Weight in Grams: 388.
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, ... Read more
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, ... Read more
Product Details
Publisher
American Mathematical Society United States
Format
Paperback
Publication date
2007
Series
Translations of Mathematical Monographs Reprint
Condition
New
Number of Pages
206
Place of Publication
Providence, United States
ISBN
9780821843024
SKU
V9780821843024
Shipping Time
Usually ships in 5 to 9 working days
Ref
99-3
About Shun-Ichi Amari (Ed.)
Shun-ichi Amari, RIKEN Brain Science Institute, Saitama, Japan Hiroshi Nagaoka, University of Electro-Communications, Tokyo, Japan
Reviews for Methods of Information Geometry
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 ... Read more