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Information geometry and its applica...

Amari, Shun-ichi.

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Information geometry and its applications

Record Type:	Electronic resources : Monograph/item
Title/Author:	Information geometry and its applications/ by Shun-ichi Amari.
Author:	Amari, Shun-ichi.
Published:	Tokyo :Springer Japan : : 2016.,
Description:	xiii, 373 p. :ill., digital ;24 cm.
[NT 15003449]:	1 Manifold, Divergence and Dually Flat Structure -- 2 Exponential Families and Mixture Families of Probability -- 3 Invariant Geometry of Manifold of Probability -- 4 α-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.
Contained By:	Springer eBooks
Subject:	Information theory - Mathematics. -
Online resource:	http://dx.doi.org/10.1007/978-4-431-55978-8
ISBN:	9784431559788$q(electronic bk.)

Information geometry and its applications
Amari, Shun-ichi.

Information geometry and its applications[electronic resource] /by Shun-ichi Amari. - Tokyo :Springer Japan :2016. - xiii, 373 p. :ill., digital ;24 cm. - Applied mathematical sciences,v.1940066-5452 ;. - Applied mathematical sciences ;v.176..

1 Manifold, Divergence and Dually Flat Structure -- 2 Exponential Families and Mixture Families of Probability -- 3 Invariant Geometry of Manifold of Probability -- 4 α-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.

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.

ISBN: 9784431559788$q(electronic bk.)

Standard No.: 10.1007/978-4-431-55978-8doiSubjects--Topical Terms:

1620355
Information theory
--Mathematics.

LC Class. No.: QA10.4

Dewey Class. No.: 510.1154

Information geometry and its applications
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100 1 $a Amari, Shun-ichi. $3 701643
245 1 0 $a Information geometry and its applications $h [electronic resource] / $c by Shun-ichi Amari.
260 $a Tokyo : $b Springer Japan : $b Imprint: Springer, $c 2016.
300 $a xiii, 373 p. : $b ill., digital ; $c 24 cm.
490 1 $a Applied mathematical sciences, $x 0066-5452 ; $v v.194
505 0 $a 1 Manifold, Divergence and Dually Flat Structure -- 2 Exponential Families and Mixture Families of Probability -- 3 Invariant Geometry of Manifold of Probability -- 4 α-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.
520 $a 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.
650 0 $a Information theory $x Mathematics. $3 1620355
650 0 $a Information theory in mathematics. $3 757432
650 0 $a Mathematical statistics. $3 516858
650 0 $a Geometry, Differential. $3 523835
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Differential Geometry. $3 891003
650 2 4 $a Mathematical Applications in Computer Science. $3 1567978
650 2 4 $a Statistical Theory and Methods. $3 891074
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830 0 $a Applied mathematical sciences ; $v v.176. $3 1565663
856 4 0 $u http://dx.doi.org/10.1007/978-4-431-55978-8
950 $a Mathematics and Statistics (Springer-11649)