Information geometry and its applications. (2016)

• Record Type: Book
• Further Information: Note: Shun-ichi Amari.
• Authors: Amari, Shun'ichi
• 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
• Publisher Details: Japan : Springer
• Publication Date: 2016
• Extent: 1 online resource (xiii, 373 pages), illustrations
• Subjects: 510.1154; Mathematics; Information theory -- Mathematics; Information theory in mathematics; Mathematical statistics; Geometry, Differential; MATHEMATICS -- Essays; MATHEMATICS -- Pre-Calculus; MATHEMATICS -- Reference; Geometry, Differential; Information theory in mathematics; Information theory -- Mathematics; Mathematical statistics; Mathematics -- Applied; Mathematics -- Probability & Statistics -- General; Mathematical modelling; Probability & statistics; Global differential geometry; Mathematics -- Geometry -- Differential; Differential & Riemannian geometry; Electronic books
• Languages: English
• ISBNs: 9784431559788; 4431559787; 4431559779; 9784431559771
• Related ISBNs: 9784431559771
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (SpringerLink, viewed February 16, 2016).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.