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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Shun?ichi Amari
Editorial: American Mathematical Society (2007)
ISBN 10: 0821843028 ISBN 13: 9780821843024
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Descripción American Mathematical Society, 2007. Paperback. Estado de conservación: New. Brand new. We distribute directly for the publisher. Clean, unmarked pages. Fine binding and cover. Ships daily. Nº de ref. de la librería 1411040072

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Shun?ichi Amari
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ISBN 10: 0821843028 ISBN 13: 9780821843024
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Descripción American Mathematical Society, 2007. Estado de conservación: New. Brand New, Unread Copy in Perfect Condition. A+ Customer Service! Summary: Elementary differential geometry The geometric structure of statistical models Dual connections Statistical inference and differential geometry The geometry of time series and linear systems Multiterminal information theory and statistical inference Information geometry for quantum systems Miscellaneous topics Guide to the bibliography Bibliography Index. Nº de ref. de la librería ABE_book_new_0821843028

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Shun?ichi Amari
Editorial: American Mathematical Society, United States (2007)
ISBN 10: 0821843028 ISBN 13: 9780821843024
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Descripción American Mathematical Society, United States, 2007. Paperback. Estado de conservación: 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. Nº de ref. de la librería AAN9780821843024

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Descripción Estado de conservación: New. Depending on your location, this item may ship from the US or UK. Nº de ref. de la librería 97808218430240000000

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Shun?ichi Amari
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Descripción American Mathematical Society, United States, 2007. Paperback. Estado de conservación: 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. Nº de ref. de la librería AAN9780821843024

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Shun?ichi Amari
Editorial: American Mathematical Society
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Descripción American Mathematical Society. Paperback. Estado de conservación: 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. Nº de ref. de la librería B9780821843024

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Shun?ichi Amari
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ISBN 10: 0821843028 ISBN 13: 9780821843024
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Descripción American Mathematical Society, 2007. Paperback. Estado de conservación: New. Nº de ref. de la librería DADAX0821843028

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Shun?ichi Amari
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Descripción American Mathematical Society, 2007. Paperback. Estado de conservación: New. book. Nº de ref. de la librería 0821843028

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Shun?ichi Amari
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Descripción Amer Mathematical Society, 2007. Paperback. Estado de conservación: Brand New. 206 pages. 9.75x6.75x0.50 inches. In Stock. Nº de ref. de la librería __0821843028

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Shun?ichi Amari
Editorial: American Mathematical Society (2007)
ISBN 10: 0821843028 ISBN 13: 9780821843024
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Descripción American Mathematical Society, 2007. Estado de conservación: 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. de la librería V9780821843024

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