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Amari, Shun-ichi

Information Geometry and Its Applications

Amari, Shun-ichi - Information Geometry and Its Applications, ebook

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Ebook, PDF with Adobe DRM
ISBN: 9784431559788
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Table of contents

Part I. Geometry of Divergence Functions: Dually Flat Riemannian Structure

1. Manifold, Divergence and Dually FlatStructure
Shun-ichi Amari

2. Exponential Families and Mixture Families of Probability Distributions
Shun-ichi Amari

3. Invariant Geometry of Manifold of Probability Distributions
Shun-ichi Amari

4.
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-Geometry, Tsallis q-Entropy andPositive-Definite Matrices
Shun-ichi Amari

Part II. Introduction to Dual Differential Geometry

5. Elements of Differential Geometry
Shun-ichi Amari

6. Dual Affine Connections and Dually Flat Manifold
Shun-ichi Amari

Part III. Information Geometry of Statistical Inference

7. Asymptotic Theory of Statistical Inference
Shun-ichi Amari

8. Estimation in the Presence of Hidden Variables
Shun-ichi Amari

9. Neyman-Scott Problem: Estimating Function and Semiparametric StatisticalModel
Shun-ichi Amari

10. Linear Systems and Time Series
Shun-ichi Amari

Part IV. Applications of Information Geometry

11. Machine Learning
Shun-ichi Amari

12. Natural Gradient Learning and Its Dynamics in Singular Regions
Shun-ichi Amari

13. Signal Processing and Optimization
Shun-ichi Amari

Keywords: Mathematics, Differential Geometry, Mathematical Applications in Computer Science, Statistical Theory and Methods

Author(s)
Publisher
Springer
Publication year
2016
Language
en
Edition
1st ed. 2016
Series
Applied Mathematical Sciences
Category
Natural Sciences
Format
Ebook
eISBN (PDF)
9784431559788
Printed ISBN
978-4-431-55977-1

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