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The Resource Information geometry and its applications, Shunichi Amari
Information geometry and its applications, Shunichi Amari
Resource Information
The item Information geometry and its applications, Shunichi Amari represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item Information geometry and its applications, Shunichi Amari represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 Summary
 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 NeymanScott 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
 Language
 eng
 Extent
 1 online resource (xiii, 373 pages)
 Contents

 Preface; Contents; Part I Geometry of Divergence Functions: Dually Flat Riemannian Structure; 1 Manifold, Divergence and Dually Flat Structure; 1.1 Manifolds; 1.1.1 Manifold and Coordinate Systems; 1.1.2 Examples of Manifolds; 1.2 Divergence Between Two Points; 1.2.1 Divergence; 1.2.2 Examples of Divergence; 1.3 Convex Function and Bregman Divergence; 1.3.1 Convex Function; 1.3.2 Bregman Divergence; 1.4 Legendre Transformation; 1.5 Dually Flat Riemannian Structure Derived from Convex Function; 1.5.1 Affine and Dual Affine Coordinate Systems
 1.5.2 Tangent Space, Basis Vectors and Riemannian Metric1.5.3 Parallel Transport of Vector; 1.6 Generalized Pythagorean Theorem and Projection Theorem; 1.6.1 Generalized Pythagorean Theorem; 1.6.2 Projection Theorem; 1.6.3 Divergence Between Submanifolds: Alternating Minimization Algorithm; 2 Exponential Families and Mixture Families of Probability Distributions; 2.1 Exponential Family of Probability Distributions; 2.2 Examples of Exponential Family: Gaussian and Discrete Distributions; 2.2.1 Gaussian Distribution; 2.2.2 Discrete Distribution; 2.3 Mixture Family of Probability Distributions
 2.4 Flat Structure: eflat and mflat2.5 On InfiniteDimensional Manifold of Probability Distributions; 2.6 Kernel Exponential Family; 2.7 Bregman Divergence and Exponential Family; 2.8 Applications of Pythagorean Theorem; 2.8.1 Maximum Entropy Principle; 2.8.2 Mutual Information; 2.8.3 Repeated Observations and Maximum Likelihood Estimator; 3 Invariant Geometry of Manifold of Probability Distributions; 3.1 Invariance Criterion; 3.2 Information Monotonicity Under Coarse Graining; 3.2.1 Coarse Graining and Sufficient Statistics in Sn; 3.2.2 Invariant Divergence
 Isbn
 9784431559788
 Label
 Information geometry and its applications
 Title
 Information geometry and its applications
 Statement of responsibility
 Shunichi Amari
 Subject

 Geometry, Differential
 Information theory in mathematics
 Electronic books
 MATHEMATICS  Reference
 Information theory in mathematics
 Geometry, Differential
 Mathematical statistics
 Information theory  Mathematics
 MATHEMATICS  Essays
 Information theory  Mathematics
 MATHEMATICS  PreCalculus
 Mathematical statistics
 Language
 eng
 Summary
 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 NeymanScott 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
 Cataloging source
 N$T
 http://library.link/vocab/creatorName
 Amari, Shun'ichi
 Dewey number
 510.1154
 Illustrations
 illustrations
 Index
 index present
 LC call number
 QA10.4
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 Applied mathematical sciences,
 Series volume
 volume 194
 http://library.link/vocab/subjectName

 Information theory
 Information theory in mathematics
 Mathematical statistics
 Geometry, Differential
 MATHEMATICS
 MATHEMATICS
 MATHEMATICS
 Geometry, Differential
 Information theory in mathematics
 Information theory
 Mathematical statistics
 Label
 Information geometry and its applications, Shunichi Amari
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents

 Preface; Contents; Part I Geometry of Divergence Functions: Dually Flat Riemannian Structure; 1 Manifold, Divergence and Dually Flat Structure; 1.1 Manifolds; 1.1.1 Manifold and Coordinate Systems; 1.1.2 Examples of Manifolds; 1.2 Divergence Between Two Points; 1.2.1 Divergence; 1.2.2 Examples of Divergence; 1.3 Convex Function and Bregman Divergence; 1.3.1 Convex Function; 1.3.2 Bregman Divergence; 1.4 Legendre Transformation; 1.5 Dually Flat Riemannian Structure Derived from Convex Function; 1.5.1 Affine and Dual Affine Coordinate Systems
 1.5.2 Tangent Space, Basis Vectors and Riemannian Metric1.5.3 Parallel Transport of Vector; 1.6 Generalized Pythagorean Theorem and Projection Theorem; 1.6.1 Generalized Pythagorean Theorem; 1.6.2 Projection Theorem; 1.6.3 Divergence Between Submanifolds: Alternating Minimization Algorithm; 2 Exponential Families and Mixture Families of Probability Distributions; 2.1 Exponential Family of Probability Distributions; 2.2 Examples of Exponential Family: Gaussian and Discrete Distributions; 2.2.1 Gaussian Distribution; 2.2.2 Discrete Distribution; 2.3 Mixture Family of Probability Distributions
 2.4 Flat Structure: eflat and mflat2.5 On InfiniteDimensional Manifold of Probability Distributions; 2.6 Kernel Exponential Family; 2.7 Bregman Divergence and Exponential Family; 2.8 Applications of Pythagorean Theorem; 2.8.1 Maximum Entropy Principle; 2.8.2 Mutual Information; 2.8.3 Repeated Observations and Maximum Likelihood Estimator; 3 Invariant Geometry of Manifold of Probability Distributions; 3.1 Invariance Criterion; 3.2 Information Monotonicity Under Coarse Graining; 3.2.1 Coarse Graining and Sufficient Statistics in Sn; 3.2.2 Invariant Divergence
 Dimensions
 unknown
 Extent
 1 online resource (xiii, 373 pages)
 File format
 unknown
 Form of item
 online
 Isbn
 9784431559788
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Note
 SpringerLink
 Other control number
 10.1007/9784431559788
 Other physical details
 illustrations.
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number

 (OCoLC)936691548
 (OCoLC)ocn936691548
 Label
 Information geometry and its applications, Shunichi Amari
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents

 Preface; Contents; Part I Geometry of Divergence Functions: Dually Flat Riemannian Structure; 1 Manifold, Divergence and Dually Flat Structure; 1.1 Manifolds; 1.1.1 Manifold and Coordinate Systems; 1.1.2 Examples of Manifolds; 1.2 Divergence Between Two Points; 1.2.1 Divergence; 1.2.2 Examples of Divergence; 1.3 Convex Function and Bregman Divergence; 1.3.1 Convex Function; 1.3.2 Bregman Divergence; 1.4 Legendre Transformation; 1.5 Dually Flat Riemannian Structure Derived from Convex Function; 1.5.1 Affine and Dual Affine Coordinate Systems
 1.5.2 Tangent Space, Basis Vectors and Riemannian Metric1.5.3 Parallel Transport of Vector; 1.6 Generalized Pythagorean Theorem and Projection Theorem; 1.6.1 Generalized Pythagorean Theorem; 1.6.2 Projection Theorem; 1.6.3 Divergence Between Submanifolds: Alternating Minimization Algorithm; 2 Exponential Families and Mixture Families of Probability Distributions; 2.1 Exponential Family of Probability Distributions; 2.2 Examples of Exponential Family: Gaussian and Discrete Distributions; 2.2.1 Gaussian Distribution; 2.2.2 Discrete Distribution; 2.3 Mixture Family of Probability Distributions
 2.4 Flat Structure: eflat and mflat2.5 On InfiniteDimensional Manifold of Probability Distributions; 2.6 Kernel Exponential Family; 2.7 Bregman Divergence and Exponential Family; 2.8 Applications of Pythagorean Theorem; 2.8.1 Maximum Entropy Principle; 2.8.2 Mutual Information; 2.8.3 Repeated Observations and Maximum Likelihood Estimator; 3 Invariant Geometry of Manifold of Probability Distributions; 3.1 Invariance Criterion; 3.2 Information Monotonicity Under Coarse Graining; 3.2.1 Coarse Graining and Sufficient Statistics in Sn; 3.2.2 Invariant Divergence
 Dimensions
 unknown
 Extent
 1 online resource (xiii, 373 pages)
 File format
 unknown
 Form of item
 online
 Isbn
 9784431559788
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Note
 SpringerLink
 Other control number
 10.1007/9784431559788
 Other physical details
 illustrations.
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number

 (OCoLC)936691548
 (OCoLC)ocn936691548
Subject
 Electronic books
 Geometry, Differential
 Geometry, Differential
 Information theory  Mathematics
 Information theory  Mathematics
 Information theory in mathematics
 Information theory in mathematics
 MATHEMATICS  Essays
 MATHEMATICS  PreCalculus
 MATHEMATICS  Reference
 Mathematical statistics
 Mathematical statistics
Genre
Member of
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