# Methods of Information Geometry (amsns AMS non-series title)

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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.

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## 1.Methods of Information Geometry (Paperback)

Publicado por American Mathematical Society, United States (2007)
ISBN 10: 0821843028 ISBN 13: 9780821843024
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The Book Depository
(London, Reino Unido)
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Descripción American Mathematical Society, United States, 2007. Paperback. Condición: New. UK ed.. Language: English . Brand New Book. 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. Nº de ref. del artículo: AAN9780821843024

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## 2.Methods of Information Geometry (Translations of Mathematical Monographs)

ISBN 10: 0821843028 ISBN 13: 9780821843024
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THE SAINT BOOKSTORE
(Southport, Reino Unido)
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Descripción American Mathematical Society. Paperback. Condición: New. New copy - Usually dispatched within 2 working days. Nº de ref. del artículo: B9780821843024

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## 3.Methods of Information Geometry (Translations of Mathematical Monographs) (Tanslations of Mathematical Monographs)

Publicado por American Mathematical Society (2007)
ISBN 10: 0821843028 ISBN 13: 9780821843024
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Ergodebooks
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Descripción American Mathematical Society, 2007. Paperback. Condición: New. Nº de ref. del artículo: DADAX0821843028

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## 4.Methods of Information Geometry (Paperback)

Publicado por American Mathematical Society, United States (2007)
ISBN 10: 0821843028 ISBN 13: 9780821843024
Librería
Book Depository International
(London, Reino Unido)
Valoración

Descripción American Mathematical Society, United States, 2007. Paperback. Condición: New. UK ed.. Language: English . Brand New Book. 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. Nº de ref. del artículo: AAN9780821843024

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## 5.Methods of Information Geometry (Translations of Mathematical Monographs) (Tanslations of Mathematical Monographs)

Publicado por American Mathematical Society 2007-04-13 (2007)
ISBN 10: 0821843028 ISBN 13: 9780821843024
Librería
Lost Books
(AUSTIN, TX, Estados Unidos de America)
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Descripción American Mathematical Society 2007-04-13, 2007. Paperback. Condición: New. 0821843028. Nº de ref. del artículo: 532565

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## 6.Methods of Information Geometry (Tanslations of Mathematical Monographs)

Publicado por Amer Mathematical Society (2007)
ISBN 10: 0821843028 ISBN 13: 9780821843024
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Revaluation Books
(Exeter, Reino Unido)
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Descripción Amer Mathematical Society, 2007. Paperback. Condición: Brand New. uk ed. edition. 206 pages. 9.75x6.75x0.50 inches. In Stock. Nº de ref. del artículo: __0821843028

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## 7.Methods of Information Geometry

Publicado por American Mathematical Society (2007)
ISBN 10: 0821843028 ISBN 13: 9780821843024
Nuevo Tapa blanda Cantidad disponible: 1
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Valoración

Descripción American Mathematical Society, 2007. Condición: New. 2007. 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. . . . . . . Nº de ref. del artículo: V9780821843024

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## 8.Methods of Information Geometry

ISBN 10: 0821843028 ISBN 13: 9780821843024
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Ria Christie Collections
(Uxbridge, Reino Unido)
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Descripción Paperback. Condición: New. Not Signed; 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. book. Nº de ref. del artículo: ria9780821843024_rkm

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## 9.Methods of Information Geometry (Translations of Mathematical Monographs) (Tanslations of Mathematical Monographs)

Publicado por American Mathematical Society (2007)
ISBN 10: 0821843028 ISBN 13: 9780821843024
Librería
Irish Booksellers
(Portland, ME, Estados Unidos de America)
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Descripción American Mathematical Society, 2007. Paperback. Condición: New. book. Nº de ref. del artículo: M0821843028

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## 10.Methods of Information Geometry

ISBN 10: 0821843028 ISBN 13: 9780821843024
Nuevo Tapa blanda Cantidad disponible: 1
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Kennys Bookstore
(Olney, MD, Estados Unidos de America)
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Descripción American Mathematical Society. Condición: New. 2007. 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. . . . . . Books ship from the US and Ireland. Nº de ref. del artículo: V9780821843024

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