Geometrical Foundations Of Asymptotic Inference
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Geometrical Foundations Of Asymptotic Inference
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Author : Robert E. Kass
language : en
Publisher: John Wiley & Sons
Release Date : 2011-09-09
Geometrical Foundations Of Asymptotic Inference written by Robert E. Kass and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-09 with Mathematics categories.
Differential geometry provides an aesthetically appealing and oftenrevealing view of statistical inference. Beginning with anelementary treatment of one-parameter statistical models and endingwith an overview of recent developments, this is the first book toprovide an introduction to the subject that is largely accessibleto readers not already familiar with differential geometry. It alsogives a streamlined entry into the field to readers with richermathematical backgrounds. Much space is devoted to curvedexponential families, which are of interest not only because theymay be studied geometrically but also because they are analyticallyconvenient, so that results may be derived rigorously. In addition,several appendices provide useful mathematical material on basicconcepts in differential geometry. Topics covered include thefollowing: * Basic properties of curved exponential families * Elements of second-order, asymptotic theory * The Fisher-Efron-Amari theory of information loss and recovery * Jeffreys-Rao information-metric Riemannian geometry * Curvature measures of nonlinearity * Geometrically motivated diagnostics for exponential familyregression * Geometrical theory of divergence functions * A classification of and introduction to additional work in thefield
Geometric Structures Of Statistical Physics Information Geometry And Learning
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Author : Frédéric Barbaresco
language : en
Publisher: Springer Nature
Release Date : 2021-06-27
Geometric Structures Of Statistical Physics Information Geometry And Learning written by Frédéric Barbaresco and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-27 with Mathematics categories.
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.
Differential Geometrical Theory Of Statistics
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Author : Frédéric Barbaresco
language : en
Publisher: MDPI
Release Date : 2018-04-06
Differential Geometrical Theory Of Statistics written by Frédéric Barbaresco and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-06 with Computers categories.
This book is a printed edition of the Special Issue "Differential Geometrical Theory of Statistics" that was published in Entropy
Geometric Science Of Information
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Author : Frank Nielsen
language : en
Publisher: Springer
Release Date : 2013-08-19
Geometric Science 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 2013-08-19 with Computers categories.
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 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.
Applications Of Differential Geometry To Econometrics
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Author : Paul Marriott
language : en
Publisher: Cambridge University Press
Release Date : 2000-08-31
Applications Of Differential Geometry To Econometrics written by Paul Marriott and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-08-31 with Business & Economics categories.
Although geometry has always aided intuition in econometrics, more recently differential geometry has become a standard tool in the analysis of statistical models, offering a deeper appreciation of existing methodologies and highlighting the essential issues which can be hidden in an algebraic development of a problem. Originally published in 2000, this volume was an early example of the application of these techniques to econometrics. An introductory chapter provides a brief tutorial for those unfamiliar with the tools of Differential Geometry. The topics covered in the following chapters demonstrate the power of the geometric method to provide practical solutions and insight into problems of econometric inference.
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 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.
Stochastic Geometry And Its Applications
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Author : Sung Nok Chiu
language : en
Publisher: John Wiley & Sons
Release Date : 2013-06-27
Stochastic Geometry And Its Applications written by Sung Nok Chiu and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-27 with Mathematics categories.
An extensive update to a classic text Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, engineering, biology and environmental sciences. They offer successful models for the description of random two- and three-dimensional micro and macro structures and statistical methods for their analysis. The previous edition of this book has served as the key reference in its field for over 18 years and is regarded as the best treatment of the subject of stochastic geometry, both as a subject with vital applications to spatial statistics and as a very interesting field of mathematics in its own right. This edition: Presents a wealth of models for spatial patterns and related statistical methods. Provides a great survey of the modern theory of random tessellations, including many new models that became tractable only in the last few years. Includes new sections on random networks and random graphs to review the recent ever growing interest in these areas. Provides an excellent introduction to theory and modelling of point processes, which covers some very latest developments. Illustrate the forefront theory of random sets, with many applications. Adds new results to the discussion of fibre and surface processes. Offers an updated collection of useful stereological methods. Includes 700 new references. Is written in an accessible style enabling non-mathematicians to benefit from this book. Provides a companion website hosting information on recent developments in the field www.wiley.com/go/cskm Stochastic Geometry and its Applications is ideally suited for researchers in physics, materials science, biology and ecological sciences as well as mathematicians and statisticians. It should also serve as a valuable introduction to the subject for students of mathematics and statistics.
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.