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

## Shun-Ichi Amari; Hiroshi Nagaoka

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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. This volume is co-published by the AMS and Oxford University Press. The AMS has exclusive distribution rights in North America. AMS members in Europe may purchase the book from the AMS. Both the AMS and OUP have worldwide distribution rights.

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... a welcome and much needed addition to the literature on the use of differential geometry methods in statistics, information theory and control theory Mathematical Reviews

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

Editore: American Mathematical Society (2007)
ISBN 10: 0821843028 ISBN 13: 9780821843024
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Descrizione libro American Mathematical Society, 2007. Paperback. Condizione libro: New. Brand new. We distribute directly for the publisher. Clean, unmarked pages. Fine binding and cover. Ships daily. Codice libro della libreria 1411040072

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## 2.Methods of Information Geometry (Paperback)

Editore: American Mathematical Society, United States (2007)
ISBN 10: 0821843028 ISBN 13: 9780821843024
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Descrizione libro American Mathematical Society, United States, 2007. Paperback. Condizione libro: 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. Codice libro della libreria AAN9780821843024

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

Editore: American Mathematical Society (2007)
ISBN 10: 0821843028 ISBN 13: 9780821843024
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Descrizione libro American Mathematical Society, 2007. Paperback. Condizione libro: New. book. Codice libro della libreria 0821843028

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## 4.Methods of Information Geometry (Paperback)

Editore: American Mathematical Society, United States (2007)
ISBN 10: 0821843028 ISBN 13: 9780821843024
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Descrizione libro American Mathematical Society, United States, 2007. Paperback. Condizione libro: 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. Codice libro della libreria AAN9780821843024

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

Editore: American Mathematical Society (2007)
ISBN 10: 0821843028 ISBN 13: 9780821843024
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Descrizione libro American Mathematical Society, 2007. Paperback. Condizione libro: New. Codice libro della libreria DADAX0821843028

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## 6.Methods Of Information Geometry

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Descrizione libro Condizione libro: New. Depending on your location, this item may ship from the US or UK. Codice libro della libreria 97808218430240000000

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

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ISBN 10: 0821843028 ISBN 13: 9780821843024
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Descrizione libro American Mathematical Society, 2007. Paperback. Condizione libro: NEW. 9780821843024 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Codice libro della libreria HTANDREE0630392

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

Editore: American Mathematical Society (2007)
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Descrizione libro American Mathematical Society, 2007. Condizione libro: new. Shiny and new! Expect delivery in 20 days. Codice libro della libreria 9780821843024-1

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

Editore: Amer Mathematical Society (2007)
ISBN 10: 0821843028 ISBN 13: 9780821843024
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Descrizione libro Amer Mathematical Society, 2007. Paperback. Condizione libro: Brand New. 206 pages. 9.75x6.75x0.50 inches. In Stock. Codice libro della libreria __0821843028

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## 10.Methods of Information Geometry

Editore: American Mathematical Society
ISBN 10: 0821843028 ISBN 13: 9780821843024
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Descrizione libro American Mathematical Society. Paperback. Condizione libro: new. BRAND NEW, Methods of Information Geometry, Shun-ichi Amari, Hiroshi Nagaoka, 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. Codice libro della libreria B9780821843024

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