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

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9780821843024: 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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Publicado por American Mathematical Society, United States (2007)
ISBN 10: 0821843028 ISBN 13: 9780821843024
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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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Publicado por American Mathematical Society
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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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Shun-Ichi Amari, Hiroshi Nagaoka
Publicado por American Mathematical Society (2007)
ISBN 10: 0821843028 ISBN 13: 9780821843024
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Descripción American Mathematical Society, 2007. Paperback. Condición: New. Nº de ref. del artículo: DADAX0821843028

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Publicado por American Mathematical Society, United States (2007)
ISBN 10: 0821843028 ISBN 13: 9780821843024
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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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Shun-Ichi Amari
Publicado por American Mathematical Society 2007-04-13 (2007)
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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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Publicado por Amer Mathematical Society (2007)
ISBN 10: 0821843028 ISBN 13: 9780821843024
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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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Shun-Ichi Amari, Hiroshi Nagaoka
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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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Shun-ichi Amari, Hiroshi Nagaoka
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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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Shun-Ichi Amari; Hiroshi Nagaoka
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ISBN 10: 0821843028 ISBN 13: 9780821843024
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Descripción American Mathematical Society, 2007. Paperback. Condición: New. book. Nº de ref. del artículo: M0821843028

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Shun-Ichi Amari, Hiroshi Nagaoka
Publicado por American Mathematical Society
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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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