Theory And Applications Of Information Geometry


Theory And Applications Of Information Geometry
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Theory And Applications Of Information Geometry


Theory And Applications Of Information Geometry
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Author : Brayan Cox
language : en
Publisher: Willford Press
Release Date : 2023-09-19

Theory And Applications Of Information Geometry written by Brayan Cox and has been published by Willford Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-19 with Mathematics categories.


Information geometry refers to an interdisciplinary field that studies probability theory and statistics by using methods of differential geometry. It is a general framework of dual affine connected with Riemannian manifolds. Information geometry involves the study of decision-making by using geometry which also includes modeling-fitting and pattern matching. It offers a novel approach that can be applied in many fields including physical and information sciences. Its primary goal is to research the geometrical structures that can be presented in the manifold connected with a set of probability distributions of a statistical model. Information geometry is also used to measure the degree of information integration among various terminals of a causal dynamical system. This book aims to shed light on the theory and applications of information geometry. It will also provide interesting topics for research, which interested readers can take up. This book is a resource guide for experts as well as students.



Progress In Information Geometry


Progress In Information Geometry
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Author : Frank Nielsen
language : en
Publisher: Springer Nature
Release Date : 2021-03-14

Progress In Information Geometry written by Frank Nielsen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-14 with Science categories.


This book focuses on information-geometric manifolds of structured data and models and related applied mathematics. It features new and fruitful interactions between several branches of science: Advanced Signal/Image/Video Processing, Complex Data Modeling and Analysis, Statistics on Manifolds, Topology/Machine/Deep Learning and Artificial Intelligence. The selection of applications makes the book a substantial information source, not only for academic scientist but it is also highly relevant for industry. The book project was initiated following discussions at the international conference GSI’2019 – Geometric Science of Information that was held at ENAC, Toulouse (France).



Information Geometry


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.



Methods Of Information Geometry


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.



Information Geometry And Its Applications


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.



Matrix Information Geometry


Matrix Information Geometry
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Author : Frank Nielsen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-07

Matrix Information Geometry written by Frank Nielsen 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 2012-08-07 with Technology & Engineering categories.


This book presents advances in matrix and tensor data processing in the domain of signal, image and information processing. The theoretical mathematical approaches are discusses in the context of potential applications in sensor and cognitive systems engineering. The topics and application include Information Geometry, Differential Geometry of structured Matrix, Positive Definite Matrix, Covariance Matrix, Sensors (Electromagnetic Fields, Acoustic sensors) and Applications in Cognitive systems, in particular Data Mining.



Geometric Structures Of Information


Geometric Structures Of Information
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Author : Frank Nielsen
language : en
Publisher: Springer
Release Date : 2018-11-19

Geometric Structures Of Information 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 2018-11-19 with Technology & Engineering categories.


This book focuses on information geometry manifolds of structured data/information and their advanced applications featuring new and fruitful interactions between several branches of science: information science, mathematics and physics. It addresses interrelations between different mathematical domains like shape spaces, probability/optimization & algorithms on manifolds, relational and discrete metric spaces, computational and Hessian information geometry, algebraic/infinite dimensional/Banach information manifolds, divergence geometry, tensor-valued morphology, optimal transport theory, manifold & topology learning, and applications like geometries of audio-processing, inverse problems and signal processing. The book collects the most important contributions to the conference GSI’2017 – Geometric Science of Information.



Information Geometry


Information Geometry
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Author :
language : en
Publisher: Elsevier
Release Date : 2021-09-26

Information Geometry written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-26 with Mathematics categories.


The subject of information geometry blends several areas of statistics, computer science, physics, and mathematics. The subject evolved from the groundbreaking article published by legendary statistician C.R. Rao in 1945. His works led to the creation of Cramer-Rao bounds, Rao distance, and Rao-Blackawellization. Fisher-Rao metrics and Rao distances play a very important role in geodesics, econometric analysis to modern-day business analytics. The chapters of the book are written by experts in the field who have been promoting the field of information geometry and its applications. Written by experts for users of information geometry Basics to advanced readers are equally taken care Origins and Clarity on Foundations



Geometric Theory Of Information


Geometric Theory Of Information
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Author : Frank Nielsen
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-05-08

Geometric Theory Of Information written by Frank Nielsen 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 2014-05-08 with Technology & Engineering categories.


This book brings together geometric tools and their applications for Information analysis. It collects current and many uses of in the interdisciplinary fields of Information Geometry Manifolds in Advanced Signal, Image & Video Processing, Complex Data Modeling and Analysis, Information Ranking and Retrieval, Coding, Cognitive Systems, Optimal Control, Statistics on Manifolds, Machine Learning, Speech/sound recognition and natural language treatment which are also substantially relevant for the industry.



Information Geometry And Its Applications


Information Geometry And Its Applications
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Author : Brayan Cox
language : en
Publisher: NY Research Press
Release Date : 2023-09-19

Information Geometry And Its Applications written by Brayan Cox and has been published by NY Research Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-19 with Mathematics categories.


Information geometry refers to an interdisciplinary field that studies statistics and probability theory by applying the techniques of differential geometry. It investigates statistical manifolds, which are Riemannian manifolds, where each point is a probability distribution. Information geometry offers a differential-geometric structure on manifolds that help in designing and studying statistical decision rules. It has been utilized in a variety of applications such as machine learning, quantum systems, mathematical finance, statistical inference, and neural networks. The amount of information integration within various terminals of a causal dynamical system is measured using information geometry. The amount of information lost can be measured using integrated information when a system is divided into parts and information transmission between the parts is stopped. This book provides comprehensive insights into information geometry and its applications. It presents researches and studies performed by experts across the globe. The book aims to equip students and experts with the advanced topics and upcoming concepts in this area of study.