# 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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### Otras ediciones populares con el mismo título

ISBN 10:  0821805312 ISBN 13:  9780821805312
Editorial: American Mathematical Society, 2001
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## 1.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
(RICHMOND, TX, Estados Unidos de America)
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Descripción American Mathematical Society, 2007. Paperback. Condición: New. Nº de ref. del artículo: DADAX0821843028

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## 2.Methods of Information Geometry (Paperback)

Publicado por American Mathematical Society, United States (2007)
ISBN 10: 0821843028 ISBN 13: 9780821843024
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Book Depository International
(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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## 3.Methods of Information Geometry (Paperback)

Publicado por American Mathematical Society, United States (2007)
ISBN 10: 0821843028 ISBN 13: 9780821843024
Librería
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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## 4.Methods of Information Geometry

ISBN 10: 0821843028 ISBN 13: 9780821843024
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THE SAINT BOOKSTORE
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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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## 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
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Lost Books
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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 (Translations of Mathematical Monographs) (Tanslations of Mathematical Monographs)

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

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## 7.Methods of Information Geometry (Translations of Mathematical Monographs) (Paperback)

ISBN 10: 0821843028 ISBN 13: 9780821843024
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Speedy Hen LLC
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Descripción Condición: New. Bookseller Inventory # ST0821843028. Nº de ref. del artículo: ST0821843028

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

Publicado por American Mathematical Society (2007)
ISBN 10: 0821843028 ISBN 13: 9780821843024
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Murray Media
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Descripción American Mathematical Society, 2007. Paperback. Condición: New. Never used!. Nº de ref. del artículo: P110821843028

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## 9.METHODS OF INFORMATION GEOMETRY (MMONO/191.S)

Publicado por American Mathematical Society (2007)
ISBN 10: 0821843028 ISBN 13: 9780821843024
Librería
Herb Tandree Philosophy Books
(Stroud, GLOS, Reino Unido)
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Descripción American Mathematical Society, 2007. Paperback. Condición: NEW. 9780821843024 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. For all enquiries, please contact Herb Tandree Philosophy Books directly - customer service is our primary goal. Nº de ref. del artículo: HTANDREE0630392

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## 10.Methods of Information Geometry

Publicado por American Mathematical Society 2007-04-15, Providence (2007)
ISBN 10: 0821843028 ISBN 13: 9780821843024
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Blackwell's
(Oxford, OX, Reino Unido)
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Descripción American Mathematical Society 2007-04-15, Providence, 2007. paperback. Condición: New. Nº de ref. del artículo: 9780821843024

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