Methods Of Information Geometry
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Methods Of Information Geometry
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Author : Shun-ichi Amari
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Methods Of Information Geometry written by Shun-ichi Amari and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Computers categories.
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.
Methods Of Information Geometry
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Author : Shunʼichi Amari
language : en
Publisher: American Mathematical Society(RI)
Release Date : 2000
Methods Of Information Geometry written by Shunʼichi Amari and has been published by American Mathematical Society(RI) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Geometry, Differential categories.
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 those which deal with statistics. Information geometry provides a new method applicable to various areas including information sciences and physical sciences. It has emerged from investigating the geometrical structures of the manifold of probability distributions, and has been applied successfully to statistical inference problems. However, it has been proved that information geometry opens a new paradigm useful for elucidation of information systems, intelligent systems, physical systems and mathematical systems.
Methods Of Information Geometry
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Author : Shun'ichi Amari
language : en
Publisher:
Release Date : 2000
Methods Of Information Geometry written by Shun'ichi Amari and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Geometry, Differential categories.
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 ubiquit.
Information Geometry And Its Applications
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Author : Shun-ichi Amari
language : en
Publisher: Springer
Release Date : 2016-02-02
Information Geometry And Its Applications written by Shun-ichi Amari and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-02 with Mathematics categories.
This is the first comprehensive book on information geometry, written by the founder of the field. It begins with an elementary introduction to dualistic geometry and proceeds to a wide range of applications, covering information science, engineering, and neuroscience. It consists of four parts, which on the whole can be read independently. A manifold with a divergence function is first introduced, leading directly to dualistic structure, the heart of information geometry. This part (Part I) can be apprehended without any knowledge of differential geometry. An intuitive explanation of modern differential geometry then follows in Part II, although the book is for the most part understandable without modern differential geometry. Information geometry of statistical inference, including time series analysis and semiparametric estimation (the Neyman–Scott problem), is demonstrated concisely in Part III. Applications addressed in Part IV include hot current topics in machine learning, signal processing, optimization, and neural networks. 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.
Information Geometry
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Author : Geert Verdoolaege
language : en
Publisher: MDPI
Release Date : 2019-04-04
Information Geometry written by Geert Verdoolaege and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-04 with Juvenile Nonfiction categories.
This Special Issue of the journal Entropy, titled “Information Geometry I”, contains a collection of 17 papers concerning the foundations and applications of information geometry. Based on a geometrical interpretation of probability, information geometry has become a rich mathematical field employing the methods of differential geometry. It has numerous applications to data science, physics, and neuroscience. Presenting original research, yet written in an accessible, tutorial style, this collection of papers will be useful for scientists who are new to the field, while providing an excellent reference for the more experienced researcher. Several papers are written by authorities in the field, and topics cover the foundations of information geometry, as well as applications to statistics, Bayesian inference, machine learning, complex systems, physics, and neuroscience.
Computational Information Geometry
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Author : Frank Nielsen
language : en
Publisher: Springer
Release Date : 2016-11-24
Computational Information Geometry written by Frank Nielsen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-24 with Technology & Engineering categories.
This book focuses on the application and development of information geometric methods in the analysis, classification and retrieval of images and signals. It provides introductory chapters to help those new to information geometry and applies the theory to several applications. This area has developed rapidly over recent years, propelled by the major theoretical developments in information geometry, efficient data and image acquisition and the desire to process and interpret large databases of digital information. The book addresses both the transfer of methodology to practitioners involved in database analysis and in its efficient computational implementation.
Information Geometry
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Author : Nihat Ay
language : en
Publisher: Springer
Release Date : 2017-08-25
Information Geometry written by Nihat Ay and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-25 with Mathematics categories.
The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional. Based on these models, canonical tensor fields are introduced and further studied, including the Fisher metric and the Amari-Chentsov tensor, and embeddings of statistical manifolds are investigated. This novel foundation then leads to application highlights, such as generalizations and extensions of the classical uniqueness result of Chentsov or the Cramér-Rao inequality. Additionally, several new application fields of information geometry are highlighted, for instance hierarchical and graphical models, complexity theory, population genetics, or Markov Chain Monte Carlo. The book will be of interest to mathematicians who are interested in geometry, information theory, or the foundations of statistics, to statisticians as well as to scientists interested in the mathematical foundations of complex systems.
Information Geometry
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Author : Khadiga Arwini
language : en
Publisher: Springer
Release Date : 2008-07-19
Information Geometry written by Khadiga Arwini and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-19 with Mathematics categories.
This volume uses information geometry to give a common differential geometric framework for a wide range of illustrative applications including amino acid sequence spacings, cryptology studies, clustering of communications and galaxies, and cosmological voids.
Differential Geometrical Methods In Statistics
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Author : Shun-ichi Amari
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Differential Geometrical Methods In Statistics written by Shun-ichi Amari and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
From the reviews: "In this Lecture Note volume the author describes his differential-geometric approach to parametrical statistical problems summarizing the results he had published in a series of papers in the last five years. The author provides a geometric framework for a special class of test and estimation procedures for curved exponential families. ... ... The material and ideas presented in this volume are important and it is recommended to everybody interested in the connection between statistics and geometry ..." #Metrika#1 "More than hundred references are given showing the growing interest in differential geometry with respect to statistics. The book can only strongly be recommended to a geodesist since it offers many new insights into statistics on a familiar ground." #Manuscripta Geodaetica#2
Information Geometry And Population Genetics
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Author : Julian Hofrichter
language : en
Publisher: Springer
Release Date : 2017-02-23
Information Geometry And Population Genetics written by Julian Hofrichter and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-23 with Mathematics categories.
The present monograph develops a versatile and profound mathematical perspective of the Wright--Fisher model of population genetics. This well-known and intensively studied model carries a rich and beautiful mathematical structure, which is uncovered here in a systematic manner. In addition to approaches by means of analysis, combinatorics and PDE, a geometric perspective is brought in through Amari's and Chentsov's information geometry. This concept allows us to calculate many quantities of interest systematically; likewise, the employed global perspective elucidates the stratification of the model in an unprecedented manner. Furthermore, the links to statistical mechanics and large deviation theory are explored and developed into powerful tools. Altogether, the manuscript provides a solid and broad working basis for graduate students and researchers interested in this field.
