
Information Geometry and Its Applications
Shun-ichi Amari(Author)
Springer (Publisher)
1st Edition
Published on 10. February 2016
Book
Hardback
XIII, 374 pages
978-4-431-55977-1 (ISBN)
Description
This is the first comprehensive book on information geometry, written by the founder of the field. It begins with an elementary introduction to dualistic geometry and proceeds to a wide range of applications, covering information science, engineering, and neuroscience. It consists of four parts, which on the whole can be read independently. A manifold with a divergence function is first introduced, leading directly to dualistic structure, the heart of information geometry. This part (Part I) can be apprehended without any knowledge of differential geometry. An intuitive explanation of modern differential geometry then follows in Part II, although the book is for the most part understandable without modern differential geometry. Information geometry of statistical inference, including time series analysis and semiparametric estimation (the Neyman-Scott problem), is demonstrated concisely in Part III. Applications addressed in Part IV include hot current topics in machine learning,signal processing, optimization, and neural networks. The book is interdisciplinary, connecting mathematics, information sciences, physics, and neurosciences, inviting readers to a new world of information and geometry. This book is highly recommended to graduate students and researchers who seek new mathematical methods and tools useful in their own fields.
Reviews / Votes
"This book gives a reasonably accessible introduction to the subject and then considers various applications. . The book provides a nice introduction to the subject. . the book provides a nice introduction to a difficult subject that has many important applications." (Marvin H. J. Gruber, Technometrics, Vol. 58 (4), April, 2016)More details
Series
Edition
1st ed. 2016
Language
English
Place of publication
Tokyo
Japan
Target group
Professional and scholarly
Research
Illustrations
98 s/w Abbildungen
XIII, 374 p. 98 illus.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 27 mm
Weight
752 gr
ISBN-13
978-4-431-55977-1 (9784431559771)
DOI
10.1007/978-4-431-55978-8
Schweitzer Classification
Other editions
Additional editions

Shun-ichi Amari
Information Geometry and Its Applications
Book
03/2018
Springer
€139.09
Shipment within 10-15 days

Shun-ichi Amari
Information Geometry and Its Applications
E-Book
02/2016
Springer
€128.39
Available for download
Content
1 Manifold, Divergence and Dually Flat Structure.- 2 Exponential Families and Mixture Families of Probability.- 3 Invariant Geometry of Manifold of Probability.- 4 a-Geometry, Tsallis q-Entropy and Positive-Definite.- 5 Elements of Differential Geometry.- 6 Dual Affine Connections and Dually Flat Manifold.- 7 Asymptotic Theory of Statistical Inference.- 8 Estimation in the Presence of Hidden Variables.- 9 Neyman-Scott Problem.- 10 Linear Systems and Time Series.- 11 Machine Learning.- 12 Natural Gradient Learning and its Dynamics in Singular.- 13 Signal Processing and Optimization.- Index.