The Resource Information geometry and its applications, Shun-ichi Amari

Information geometry and its applications, Shun-ichi Amari

Label
Information geometry and its applications
Title
Information geometry and its applications
Statement of responsibility
Shun-ichi Amari
Creator
Author
Subject
Genre
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 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
Member of
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, Shun-ichi Amari
Link
https://ezproxy.lib.ou.edu/login?url=http://link.springer.com/10.1007/978-4-431-55978-8
Instantiates
Publication
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: e-flat and m-flat2.5 On Infinite-Dimensional 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
10.1007/978-4-431-55978-8
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, Shun-ichi Amari
Link
https://ezproxy.lib.ou.edu/login?url=http://link.springer.com/10.1007/978-4-431-55978-8
Publication
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: e-flat and m-flat2.5 On Infinite-Dimensional 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
10.1007/978-4-431-55978-8
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

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