Information Geometry And Its Applications

Author by : Shun-ichi Amari
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
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Description : 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.


Methods Of Information Geometry

Author by : Shun-ichi Amari
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 96
Total Download : 794
File Size : 52,6 Mb
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Description : 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.


Information Geometry

Author by : Khadiga Arwini
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 32
Total Download : 159
File Size : 48,8 Mb
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Description : This volume will be useful to practising scientists and students working in the application of statistical models to real materials or to processes with perturbations of a Poisson process, a uniform process, or a state of independence for a bivariate process. We use information geometry to provide a common differential geometric framework for a wide range of illustrative applications including amino acid sequence spacings in protein chains, cryptology studies, clustering of communications and galaxies, cosmological voids, coupled spatial statistics in stochastic fibre networks and stochastic porous media, quantum chaology. Introduction sections are provided to mathematical statistics, differential geometry and the information geometry of spaces of probability density functions.


Information Geometry

Author by : Geert Verdoolaege
Languange : en
Publisher by : MDPI
Format Available : PDF, ePub, Mobi
Total Read : 31
Total Download : 748
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Description : 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.


Information Geometry

Author by : Nihat Ay
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 58
Total Download : 653
File Size : 46,9 Mb
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Description : 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.


Progress In Information Geometry

Author by : Frank Nielsen
Languange : en
Publisher by : Springer Nature
Format Available : PDF, ePub, Mobi
Total Read : 66
Total Download : 187
File Size : 45,5 Mb
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Description : 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).


Matrix Information Geometry

Author by : Frank Nielsen
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 16
Total Download : 491
File Size : 54,7 Mb
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Description : 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.


Information Geometry

Author by : Anonim
Languange : en
Publisher by : Elsevier
Format Available : PDF, ePub, Mobi
Total Read : 32
Total Download : 513
File Size : 44,7 Mb
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Description : 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


Information Geometry

Author by : Khadiga Arwini
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 67
Total Download : 152
File Size : 44,8 Mb
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Description : 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.


Computational Information Geometry

Author by : Frank Nielsen
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 57
Total Download : 258
File Size : 40,9 Mb
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Description : 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 And Its Applications

Author by : Nihat Ay
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 58
Total Download : 756
File Size : 40,5 Mb
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Description : The book gathers contributions from the fourth conference on Information Geometry and its Applications, which was held on June 12–17, 2016, at Liblice Castle, Czech Republic on the occasion of Shun-ichi Amari’s 80th birthday and was organized by the Czech Academy of Sciences’ Institute of Information Theory and Automation. The conference received valuable financial support from the Max Planck Institute for Mathematics in the Sciences (Information Theory of Cognitive Systems Group), Czech Academy of Sciences’ Institute of Information Theory and Automation, and Università degli Studi di Roma Tor Vergata. The aim of the conference was to highlight recent advances in the field of information geometry and to identify new research directions. To this end, the event brought together leading experts in the field who, in invited talks and poster sessions, discussed both theoretical work and achievements in the many fields of application in which information geometry plays an essential role.


Information Geometry And Population Genetics

Author by : Julian Hofrichter
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 84
Total Download : 495
File Size : 44,7 Mb
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Description : 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.


Geometric Science Of Information

Author by : Frank Nielsen
Languange : en
Publisher by : Springer Nature
Format Available : PDF, ePub, Mobi
Total Read : 71
Total Download : 415
File Size : 55,6 Mb
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Description : This book constitutes the proceedings of the 5th International Conference on Geometric Science of Information, GSI 2021, held in Paris, France, in July 2021. The 98 papers presented in this volume were carefully reviewed and selected from 125 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications. The papers are organized in the following topics: Probability and statistics on Riemannian Manifolds; sub-Riemannian geometry and neuromathematics; shapes spaces; geometry of quantum states; geometric and structure preserving discretizations; information geometry in physics; Lie group machine learning; geometric and symplectic methods for hydrodynamical models; harmonic analysis on Lie groups; statistical manifold and Hessian information geometry; geometric mechanics; deformed entropy, cross-entropy, and relative entropy; transformation information geometry; statistics, information and topology; geometric deep learning; topological and geometrical structures in neurosciences; computational information geometry; manifold and optimization; divergence statistics; optimal transport and learning; and geometric structures in thermodynamics and statistical physics.


Geometric Science Of Information

Author by : Frank Nielsen
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 89
Total Download : 477
File Size : 40,8 Mb
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Description : This book constitutes the refereed proceedings of the First International Conference on Geometric Science of Information, GSI 2013, held in Paris, France, in August 2013. The nearly 100 papers presented were carefully reviewed and selected from numerous submissions and are organized into the following thematic sessions: Geometric Statistics on Manifolds and Lie Groups, Deformations in Shape Spaces, Differential Geometry in Signal Processing, Relational Metric, Discrete Metric Spaces, Computational Information Geometry, Hessian Information Geometry I and II, Computational Aspects of Information Geometry in Statistics, Optimization on Matrix Manifolds, Optimal Transport Theory, Probability on Manifolds, Divergence Geometry and Ancillarity, Entropic Geometry, Tensor-Valued Mathematical Morphology, Machine/Manifold/Topology Learning, Geometry of Audio Processing, Geometry of Inverse Problems, Algebraic/Infinite dimensional/Banach Information Manifolds, Information Geometry Manifolds, and Algorithms on Manifolds.


Geometric Structures Of Information

Author by : Frank Nielsen
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 53
Total Download : 405
File Size : 52,5 Mb
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Description : 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.


Geometric Theory Of Information

Author by : Frank Nielsen
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 71
Total Download : 399
File Size : 48,5 Mb
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Description : 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.


Geometric Structures Of Statistical Physics Information Geometry And Learning

Author by : Frédéric Barbaresco
Languange : en
Publisher by : Springer Nature
Format Available : PDF, ePub, Mobi
Total Read : 29
Total Download : 153
File Size : 42,6 Mb
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Description : Machine learning and artificial intelligence increasingly use methodological tools rooted in statistical physics. Conversely, limitations and pitfalls encountered in AI question the very foundations of statistical physics. This interplay between AI and statistical physics has been attested since the birth of AI, and principles underpinning statistical physics can shed new light on the conceptual basis of AI. During the last fifty years, statistical physics has been investigated through new geometric structures allowing covariant formalization of the thermodynamics. Inference methods in machine learning have begun to adapt these new geometric structures to process data in more abstract representation spaces. This volume collects selected contributions on the interplay of statistical physics and artificial intelligence. The aim is to provide a constructive dialogue around a common foundation to allow the establishment of new principles and laws governing these two disciplines in a unified manner. The contributions were presented at the workshop on the Joint Structures and Common Foundation of Statistical Physics, Information Geometry and Inference for Learning which was held in Les Houches in July 2020. The various theoretical approaches are discussed in the context of potential applications in cognitive systems, machine learning, signal processing.


Geometry And Nature

Author by : William Kingdon Clifford
Languange : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 41
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Description : This volume is the outgrowth of a conference devoted to William K. Clifford entitled, 'New Trends in Geometrical and Topological Methods', which was held at the University of Madeira in July and August 1995. The aim of the conference was to bring together active workers in fields linked to Clifford's work and to foster the exchange of ideas between mathematicians and theoretical physicists. Divided into 6 one-day sessions, each session was devoted to a specific aspect of Clifford's work. This volume is an attempt to bring the Clifford legacy in a new perspective to a larger community of mathematicians and physicists. New concepts, ideas, and results stemming from Clifford's work are discussed. Each article in the book is a self-contained paper that was presented at or submitted to the conference.


J H Kika No H H

Author by : Shunʼichi Amari
Languange : en
Publisher by : Amer Mathematical Society
Format Available : PDF, ePub, Mobi
Total Read : 56
Total Download : 927
File Size : 49,7 Mb
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Description : 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.


Information Geometry A Complete Guide 2019 Edition

Author by : Gerardus Blokdyk
Languange : en
Publisher by : 5starcooks
Format Available : PDF, ePub, Mobi
Total Read : 35
Total Download : 356
File Size : 54,7 Mb
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Description : How could quantum physics potentially be useful in information technology? Does machine learning support high availability? What level of data loss is acceptable? What obstacles to success can you foresee? How was amplitude inspired by ai or machine learning to deliver product analytics value? This exclusive Information Geometry self-assessment will make you the accepted Information Geometry domain assessor by revealing just what you need to know to be fluent and ready for any Information Geometry challenge. How do I reduce the effort in the Information Geometry work to be done to get problems solved? How can I ensure that plans of action include every Information Geometry task and that every Information Geometry outcome is in place? How will I save time investigating strategic and tactical options and ensuring Information Geometry costs are low? How can I deliver tailored Information Geometry advice instantly with structured going-forward plans? There's no better guide through these mind-expanding questions than acclaimed best-selling author Gerard Blokdyk. Blokdyk ensures all Information Geometry essentials are covered, from every angle: the Information Geometry self-assessment shows succinctly and clearly that what needs to be clarified to organize the required activities and processes so that Information Geometry outcomes are achieved. Contains extensive criteria grounded in past and current successful projects and activities by experienced Information Geometry practitioners. Their mastery, combined with the easy elegance of the self-assessment, provides its superior value to you in knowing how to ensure the outcome of any efforts in Information Geometry are maximized with professional results. Your purchase includes access details to the Information Geometry self-assessment dashboard download which gives you your dynamically prioritized projects-ready tool and shows you exactly what to do next. Your exclusive instant access details can be found in your book. You will receive the following contents with New and Updated specific criteria: - The latest quick edition of the book in PDF - The latest complete edition of the book in PDF, which criteria correspond to the criteria in... - The Self-Assessment Excel Dashboard - Example pre-filled Self-Assessment Excel Dashboard to get familiar with results generation - In-depth and specific Information Geometry Checklists - Project management checklists and templates to assist with implementation INCLUDES LIFETIME SELF ASSESSMENT UPDATES Every self assessment comes with Lifetime Updates and Lifetime Free Updated Books. Lifetime Updates is an industry-first feature which allows you to receive verified self assessment updates, ensuring you always have the most accurate information at your fingertips.


Regression Estimators

Author by : Marvin H. J. Gruber
Languange : en
Publisher by : JHU Press
Format Available : PDF, ePub, Mobi
Total Read : 63
Total Download : 215
File Size : 45,8 Mb
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Description : Praise for the first edition --


Geometric Science Of Information

Author by : Frank Nielsen
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 94
Total Download : 489
File Size : 46,5 Mb
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Description : This book constitutes the proceedings of the 5th International Conference on Geometric Science of Information, GSI 2021, held in Paris, France, in July 2021. The 98 papers presented in this volume were carefully reviewed and selected from 125 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications. The papers are organized in the following topics: Probability and statistics on Riemannian Manifolds; sub-Riemannian geometry and neuromathematics; shapes spaces; geometry of quantum states; geometric and structure preserving discretizations; information geometry in physics; Lie group machine learning; geometric and symplectic methods for hydrodynamical models; harmonic analysis on Lie groups; statistical manifold and Hessian information geometry; geometric mechanics; deformed entropy, cross-entropy, and relative entropy; transformation information geometry; statistics, information and topology; geometric deep learning; topological and geometrical structures in neurosciences; computational information geometry; manifold and optimization; divergence statistics; optimal transport and learning; and geometric structures in thermodynamics and statistical physics.


Innovations In Bayesian Networks

Author by : Dawn E. Holmes
Languange : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 27
Total Download : 820
File Size : 48,5 Mb
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Description : Bayesian networks currently provide one of the most rapidly growing areas of research in computer science and statistics. In compiling this volume we have brought together contributions from some of the most prestigious researchers in this field. Each of the twelve chapters is self-contained. Both theoreticians and application scientists/engineers in the broad area of artificial intelligence will find this volume valuable. It also provides a useful sourcebook for Graduate students since it shows the direction of current research.


Neural Information Processing

Author by : Tom Gedeon
Languange : en
Publisher by : Springer Nature
Format Available : PDF, ePub, Mobi
Total Read : 20
Total Download : 687
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Description : The two-volume set CCIS 1142 and 1143 constitutes thoroughly refereed contributions presented at the 26th International Conference on Neural Information Processing, ICONIP 2019, held in Sydney, Australia, in December 2019. For ICONIP 2019 a total of 345 papers was carefully reviewed and selected for publication out of 645 submissions. The 168 papers included in this volume set were organized in topical sections as follows: adversarial networks and learning; convolutional neural networks; deep neural networks; embeddings and feature fusion; human centred computing; human centred computing and medicine; human centred computing for emotion; hybrid models; image processing by neural techniques; learning from incomplete data; model compression and optimization; neural network applications; neural network models; semantic and graph based approaches; social network computing; spiking neuron and related models; text computing using neural techniques; time-series and related models; and unsupervised neural models.


Differential Geometry And Statistics

Author by : M.K. Murray
Languange : en
Publisher by : CRC Press
Format Available : PDF, ePub, Mobi
Total Read : 45
Total Download : 380
File Size : 48,9 Mb
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Description : Ever since the introduction by Rao in 1945 of the Fisher information metric on a family of probability distributions, there has been interest among statisticians in the application of differential geometry to statistics. This interest has increased rapidly in the last couple of decades with the work of a large number of researchers. Until now an impediment to the spread of these ideas into the wider community of statisticians has been the lack of a suitable text introducing the modern coordinate free approach to differential geometry in a manner accessible to statisticians. Differential Geometry and Statistics aims to fill this gap. The authors bring to this book extensive research experience in differential geometry and its application to statistics. The book commences with the study of the simplest differentiable manifolds - affine spaces and their relevance to exponential families, and goes on to the general theory, the Fisher information metric, the Amari connections and asymptotics. It culminates in the theory of vector bundles, principal bundles and jets and their applications to the theory of strings - a topic presently at the cutting edge of research in statistics and differential geometry.


Operations Research Engineering And Cyber Security

Author by : Nicholas J. Daras
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 53
Total Download : 759
File Size : 49,5 Mb
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Description : Mathematical methods and theories with interdisciplinary applications are presented in this book. The eighteen contributions presented in this Work have been written by eminent scientists; a few papers are based on talks which took place at the International Conference at the Hellenic Artillery School in May 2015. Each paper evaluates possible solutions to long-standing problems such as the solvability of the direct electromagnetic scattering problem, geometric approaches to cyber security, ellipsoid targeting with overlap, non-equilibrium solutions of dynamic networks, measuring ballistic dispersion, elliptic regularity theory for the numerical solution of variational problems, approximation theory for polynomials on the real line and the unit circle, complementarity and variational inequalities in electronics, new two-slope parameterized achievement scalarizing functions for nonlinear multiobjective optimization, and strong and weak convexity of closed sets in a Hilbert space. /divGraduate students, scientists, engineers and researchers in pure and applied mathematical sciences, operations research, engineering, and cyber security will find the interdisciplinary scientific perspectives useful to their overall understanding and further research.


Emerging Trends In Visual Computing

Author by : Frank Nielsen
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 83
Total Download : 487
File Size : 49,7 Mb
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Description : This book features contributions from the LIX Fall Colloquium on the Emerging Trends in Visual Computing, ETVC 2008. Coverage includes information geometry and applications, computer graphics and vision, and medical imaging and computational anatomy.


Engineering General Intelligence Part 2

Author by : Ben Goertzel
Languange : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 10
Total Download : 591
File Size : 43,7 Mb
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Description : The work outlines a detailed blueprint for the creation of an Artificial General Intelligence system with capability at the human level and ultimately beyond, according to the Cog Prime AGI design and the Open Cog software architecture.