# Methods of Information Geometry

## Shun?ichi Amari

Valutazione media 4,6
( su 5 valutazioni fornite da GoodReads )

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.

Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.

Compra nuovo Guarda l'articolo
EUR 65,77

Spese di spedizione: EUR 3,70
In U.S.A.

Destinazione, tempi e costi

Aggiungere al carrello

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

Editore: American Mathematical Society (2007)
ISBN 10: 0821843028 ISBN 13: 9780821843024
Nuovi Paperback Quantità: > 20
Da
Sequitur Books
(Boonsboro, MD, U.S.A.)
Valutazione libreria

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

Compra nuovo
EUR 65,77
Convertire valuta
Spese di spedizione: EUR 3,70
In U.S.A.
Destinazione, tempi e costi

## 2.Methods of Information Geometry (Paperback)

Editore: American Mathematical Society, United States (2007)
ISBN 10: 0821843028 ISBN 13: 9780821843024
Nuovi Paperback Quantità: 10
Da
The Book Depository US
(London, Regno Unito)
Valutazione libreria

Descrizione libro American Mathematical Society, United States, 2007. Paperback. Condizione libro: New. 251 x 183 mm. 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

Compra nuovo
EUR 83,76
Convertire valuta
Spese di spedizione: GRATIS
Da: Regno Unito a: U.S.A.
Destinazione, tempi e costi

## 3.Methods Of Information Geometry

ISBN 10: 0821843028 ISBN 13: 9780821843024
Nuovi Quantità: 10
Da
BWB
(Valley Stream, NY, U.S.A.)
Valutazione libreria

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

Compra nuovo
EUR 84,10
Convertire valuta
Spese di spedizione: GRATIS
In U.S.A.
Destinazione, tempi e costi

## 4.Methods of Information Geometry (Paperback)

Editore: American Mathematical Society, United States (2007)
ISBN 10: 0821843028 ISBN 13: 9780821843024
Nuovi Paperback Quantità: 10
Da
The Book Depository
(London, Regno Unito)
Valutazione libreria

Descrizione libro American Mathematical Society, United States, 2007. Paperback. Condizione libro: New. 251 x 183 mm. 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

Compra nuovo
EUR 85,66
Convertire valuta
Spese di spedizione: GRATIS
Da: Regno Unito a: U.S.A.
Destinazione, tempi e costi

## 5.Methods of Information Geometry

Editore: American Mathematical Society
ISBN 10: 0821843028 ISBN 13: 9780821843024
Nuovi Paperback Quantità: 9
Da
THE SAINT BOOKSTORE
(Southport, Regno Unito)
Valutazione libreria

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

Compra nuovo
EUR 82,40
Convertire valuta
Spese di spedizione: EUR 6,86
Da: Regno Unito a: U.S.A.
Destinazione, tempi e costi

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

Editore: American Mathematical Society 2007-04-13 (2007)
ISBN 10: 0821843028 ISBN 13: 9780821843024
Nuovi Paperback Quantità: 1
Da
Lost Books
(AUSTIN, TX, U.S.A.)
Valutazione libreria

Descrizione libro American Mathematical Society 2007-04-13, 2007. Paperback. Condizione libro: New. 0821843028. Codice libro della libreria 532565

Compra nuovo
EUR 89,71
Convertire valuta
Spese di spedizione: EUR 3,69
In U.S.A.
Destinazione, tempi e costi

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

Editore: American Mathematical Society (2007)
ISBN 10: 0821843028 ISBN 13: 9780821843024
Nuovi Paperback Quantità: 1
Da
Irish Booksellers
(Rumford, ME, U.S.A.)
Valutazione libreria

Descrizione libro American Mathematical Society, 2007. Paperback. Condizione libro: New. book. Codice libro della libreria 0821843028

Compra nuovo
EUR 95,36
Convertire valuta
Spese di spedizione: GRATIS
In U.S.A.
Destinazione, tempi e costi

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

Editore: American Mathematical Society (2007)
ISBN 10: 0821843028 ISBN 13: 9780821843024
Nuovi Paperback Quantità: 1
Da
Herb Tandree Philosophy Books
(Stroud, GLOS, Regno Unito)
Valutazione libreria

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

Compra nuovo
EUR 100,46
Convertire valuta
Spese di spedizione: EUR 9,23
Da: Regno Unito a: U.S.A.
Destinazione, tempi e costi

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

Editore: Amer Mathematical Society (2007)
ISBN 10: 0821843028 ISBN 13: 9780821843024
Nuovi Paperback Quantità: 2
Da
Revaluation Books
(Exeter, Regno Unito)
Valutazione libreria

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

Compra nuovo
EUR 110,96
Convertire valuta
Spese di spedizione: EUR 6,93
Da: Regno Unito a: U.S.A.
Destinazione, tempi e costi

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

Editore: American Mathematical Society (2007)
ISBN 10: 0821843028 ISBN 13: 9780821843024
Nuovi Paperback Quantità: 3
Da
Murray Media
(North Miami Beach, FL, U.S.A.)
Valutazione libreria

Descrizione libro American Mathematical Society, 2007. Paperback. Condizione libro: New. Codice libro della libreria P110821843028

Compra nuovo
EUR 117,99
Convertire valuta
Spese di spedizione: EUR 2,77
In U.S.A.
Destinazione, tempi e costi