12 edition of **Methods of information geometry** found in the catalog.

- 81 Want to read
- 14 Currently reading

Published
**2000** by American Mathematical Society in Providence, RI .

Written in English

- Mathematical statistics,
- Geometry, Differential

**Edition Notes**

Includes bibliographical references (p. 187-202) and index.

Statement | Shun-ichi Amari, Hiroshi Nagaoka ; [translated from the Japanese by Daishi Harada]. |

Series | Translations of mathematical monographs -- v. 191 |

Contributions | Nagaoka, Hiroshi, 1955- |

Classifications | |
---|---|

LC Classifications | QA276 .A56313 2000 |

The Physical Object | |

Pagination | x, 206 p. : |

Number of Pages | 206 |

ID Numbers | |

Open Library | OL13628540M |

ISBN 10 | 0821805312 |

LC Control Number | 00059362 |

OCLC/WorldCa | 44613213 |

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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 $\alpha$ by: Information geometry provides a new method applicable to various areas including information sciences and physical sciences.

It has emerged from investigating the geometrical structu There has been much progress in the field of information geometry in recent years and yet there are few textbooks which reflect these developments, except for /5(8).

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.

Presents for the first time the entirety of the emerging field of information geometry this book will play a key role for the further progress of information geometry Zentralblatt MATH.

Until now there have been no expository textbooks covering the methods and applications of information geometry. This book presents the state of the art, the current best practices and the innovative techniques of the methods of information geometry.

The first half of the book presents 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. The book is interdisciplinary, connecting mathematics, information sciences, physics, and neurosciences, inviting readers to a new world of information and geometry.

This book is highly recommended to graduate students and researchers who seek new mathematical methods and tools useful in their own fields. Our method uses ideas from information geometry [15, 18, 19] to derive an update rule that incorporates the interaction between the players and.

Methods of information geometry book This book presents the state of the art, the current best practices and the innovative techniques of the methods of information geometry. The first half of the book presents 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.

– based on the book “Methods of Information Geometry ”written by Shun-Ichi Amari and Hiroshi Nagaoka Yunshu Liu Introduction to differential geometry Geometric structure of statistical models and statistical inference Outline 1 Introduction to differential geometry.

Information geometry reached maturity through the work of Shun’ichi Amari and other Japanese mathematicians in the s. Amari and Nagaoka’s book, Methods of Information Geometry, is cited by most works of the relatively young eld due to its broad coverage of signi cant developments attained using the methods of information geometry up to.

His method incorporated algebra, and opened the door for the discovery of calculus. Still, Euclidean geometry was the undisputed champ of the mathematical world until the early 19th century, when several mathematicians, including Carl Friedrich.

Information Geometry and Its Applications to Machine Learning Shun-ichi Amari RIKEN Brain Science Institute. Information Geometry-- Manifolds of Probability Distributions Mp={()}x. Information Geometry Systems Theory Information Theory Statistics Neural Networks Combinatorics Information.

Book 11 deals with the fundamental propositions of three-dimensional geometry. Book 12 calculates the relative volumes of cones, pyramids, cylinders, and spheres using the method of exhaustion.

Finally, Book 13 investigates the ﬁve so-called Platonic solids. However, information geometry is definitely a relatively niche mathematical field. Personally, I prefer things this way; information geometry gives a rich class of examples and there is relatively low-hanging fruit to be found.

As to the reason for this, in my opinion IG is really an interdisciplinary field and not simply a branch of mathematics. It connects diverse branches of mathematical sciences that deal with probability, entropy, measurement, inference, and related concepts. Coverage includes original work and synthesis exploring the foundation and application of information geometry in.

Euclidean Geometry by Rich Cochrane and Andrew McGettigan. This is a great mathematics book cover the following topics: Equilateral Triangle, Perpendicular Bisector, Angle Bisector, Angle Made by Lines, The Regular Hexagon, Addition and Subtraction of Lengths, Addition and Subtraction of Angles, Perpendicular Lines, Parallel Lines and Angles, Constructing Parallel Lines, Squares and Other.

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.

The book is interdisciplinary, connecting mathematics, information sciences, physics, and neurosciences, inviting readers to a new world of information and geometry. This book is highly recommended to graduate students and researchers who seek new mathematical methods and tools useful in their own s: 5.

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Information geometry is a new branch in mathematics, originated from the applications of differential geometry to statistics. Book. Methods of Information Geometry (Translations of. Read “mathematics books” and do mathematics.

Exercises are must. Use as many methods as you can think of, certainly including the one which is recommended. Consult the Appendix after you work out the solution.

Follow the comments, interpretations and suggested extensions. Think. Get excited. Discuss. Bore everybody in your known circles. Download PDF Abstract: To what extent can we distinguish one probability distribution from another.

Are there quantitative measures of distinguishability. The goal of this tutorial is to approach such questions by introducing the notion of the "distance" between two probability distributions and exploring some basic ideas of such an "information geometry".

Grandfather Tang’s Story: A Tale Told with Tangrams by Ann Tompert offers an interesting take on geometry instruction by incorporating tangrams into this adorable story. Tangrams can be an effective hands-on method to teach basic geometry concepts.

Not only does this book introduce the use of tangrams, but it also offers readers a beautiful story about a girl and her grandfather.

Geometry was revolutionized by Euclid, who introduced mathematical rigor and the axiomatic method still in use today. His book, The Elements is widely considered the most influential textbook of all time, and was known to all educated people in the West until the middle of the 20th century.

Madison College Textbook for College Mathematics Revised Fall of Edition. Authored by various members of the Mathematics Department of Madison Area Technical College. How to use this workbook.

Each chapter consists of text plus worked examples. These are followed by Exercises labeled as Your Turn. The first three chapters of the book provide a comprehensive introduction to the mathematical foundation of information geometry while the remaining chapters provide an overview of the scope of its application.

It is hoped that Methods of Information Geometry will become a key text in information geometry and help to inspire further. Methods of Information Geometry (Tanslations of Mathematical Monographs)的话题 (全部 条) 什么是话题 无论是一部作品、一个人，还是一件事，都往往可以衍生出许多不同的话题。. Find many great new & used options and get the best deals for [P-D-F] Optimization Methods in Finance Mathematics, Finance and Risk 2nd Editio at the best online Location: Brockton, Massachusetts.

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It has now been four decades since David Mumford wrote that algebraic ge. Some Illustrations of Information Geometry in Biology and Physics: /ch Many real processes have stochastic features which seem to be representable in some intuitive sense as `close to Poisson’, `nearly random’, `nearly uniform’.

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Additional resources for Methods of Information Geometry. book [4] can be considered as a continuation of the book [2]. It illustrates the application of diﬀerential geometry to physics. The book [5] is a brief version of the book [2]. As for the book [6], by its subject it should precede this book.

It could br recommended to the reader for deeper logical understanding of the elementary geometry. Information Geometry and Its Applications Shun‐ichi Amari RIKEN Brain Science Institute ence Function and Dually Flat Riemannian Structure ant Geometry on Manifold of Probability Distributions ry and Statistical Inference semi‐parametrics 4.

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Photos 2 & 3 show that the front cover is partially detached but the pages inside are firmly bound to the spine. Photo 12 shows a name in pen on the side of the pages when the book is closed Seller Rating: % positive.

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