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; Hiroshi Nagaoka
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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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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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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Editorial: American Mathematical Society, United States (2007)
ISBN 10: 0821843028 ISBN 13: 9780821843024
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The Book Depository
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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, Hiroshi Nagaoka
Editorial: American Mathematical Society
ISBN 10: 0821843028 ISBN 13: 9780821843024
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THE SAINT BOOKSTORE
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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; Hiroshi Nagaoka
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ISBN 10: 0821843028 ISBN 13: 9780821843024
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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, Hiroshi Nagaoka
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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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AMARI NAGAOKA
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Descripción American Mathematical Society, 2007. Paperback. Estado de conservación: NEW. 9780821843024 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Nº de ref. de la librería HTANDREE0630392

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Shun-Ichi Amari, Hiroshi Nagaoka
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Descripción American Mathematical Society, 2007. Paperback. Estado de conservación: New. Nº de ref. de la librería P110821843028

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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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