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.

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.

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.

Geometric Modeling In Probability And Statistics

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Author : Ovidiu Calin
language : en
Publisher: Springer
Release Date : 2014-07-17

Geometric Modeling In Probability And Statistics written by Ovidiu Calin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-17 with Mathematics categories.

This book covers topics of Informational Geometry, a field which deals with the differential geometric study of the manifold probability density functions. This is a field that is increasingly attracting the interest of researchers from many different areas of science, including mathematics, statistics, geometry, computer science, signal processing, physics and neuroscience. It is the authors’ hope that the present book will be a valuable reference for researchers and graduate students in one of the aforementioned fields. This textbook is a unified presentation of differential geometry and probability theory, and constitutes a text for a course directed at graduate or advanced undergraduate students interested in applications of differential geometry in probability and statistics. The book contains over 100 proposed exercises meant to help students deepen their understanding, and it is accompanied by software that is able to provide numerical computations of several information geometric objects. The reader will understand a flourishing field of mathematics in which very few books have been written so far.

Statistical Tests For Mixed Linear Models

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Author : André I. Khuri
language : en
Publisher: John Wiley & Sons
Release Date : 2011-09-09

Statistical Tests For Mixed Linear Models written by André I. Khuri 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.

An advanced discussion of linear models with mixed or randomeffects. In recent years a breakthrough has occurred in our ability todraw inferences from exact and optimum tests of variance componentmodels, generating much research activity that relies on linearmodels with mixed and random effects. This volume covers the mostimportant research of the past decade as well as the latestdevelopments in hypothesis testing. It compiles all currentlyavailable results in the area of exact and optimum tests forvariance component models and offers the only comprehensivetreatment for these models at an advanced level. Statistical Tests for Mixed Linear Models: Combines analysis and testing in one self-containedvolume. Describes analysis of variance (ANOVA) procedures in balancedand unbalanced data situations. Examines methods for determining the effect of imbalance ondata analysis. Explains exact and optimum tests and methods for theirderivation. Summarizes test procedures for multivariate mixed and randommodels. Enables novice readers to skip the derivations and discussionson optimum tests. Offers plentiful examples and exercises, manyof which are numerical in flavor. Provides solutions to selected exercises. Statistical Tests for Mixed Linear Models is an accessiblereference for researchers in analysis of variance, experimentaldesign, variance component analysis, and linear mixed models. It isalso an important text for graduate students interested in mixedmodels.

Probability For Statistics And Machine Learning

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Author : Anirban DasGupta
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-17

Probability For Statistics And Machine Learning written by Anirban DasGupta 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 2011-05-17 with Mathematics categories.

This book provides a versatile and lucid treatment of classic as well as modern probability theory, while integrating them with core topics in statistical theory and also some key tools in machine learning. It is written in an extremely accessible style, with elaborate motivating discussions and numerous worked out examples and exercises. The book has 20 chapters on a wide range of topics, 423 worked out examples, and 808 exercises. It is unique in its unification of probability and statistics, its coverage and its superb exercise sets, detailed bibliography, and in its substantive treatment of many topics of current importance. This book can be used as a text for a year long graduate course in statistics, computer science, or mathematics, for self-study, and as an invaluable research reference on probabiliity and its applications. Particularly worth mentioning are the treatments of distribution theory, asymptotics, simulation and Markov Chain Monte Carlo, Markov chains and martingales, Gaussian processes, VC theory, probability metrics, large deviations, bootstrap, the EM algorithm, confidence intervals, maximum likelihood and Bayes estimates, exponential families, kernels, and Hilbert spaces, and a self contained complete review of univariate probability.