Information Geometry and Its Applications

• Κύριος συγγραφέας: Amari, Shun-ichi (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Tokyo : Springer Japan : Imprint: Springer, 2016.
• Έκδοση: 1st ed. 2016.
• Σειρά: Applied Mathematical Sciences, 194
• Θέματα: Mathematics.; Computer science > Mathematics.; Computer mathematics.; Differential geometry.; Statistics.; Differential Geometry.; Mathematical Applications in Computer Science.; Statistical Theory and Methods.

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, whi...

Πίνακας περιεχομένων:

• 1 Manifold, Divergence and Dually Flat Structure
• 2 Exponential Families and Mixture Families of Probability
• 3 Invariant Geometry of Manifold of Probability
• 4 α-Geometry, Tsallis q-Entropy and Positive-Definite
• 5 Elements of Differential Geometry
• 6 Dual Affine Connections and Dually Flat Manifold
• 7 Asymptotic Theory of Statistical Inference
• 8 Estimation in the Presence of Hidden Variables
• 9 Neyman–Scott Problem
• 10 Linear Systems and Time Series
• 11 Machine Learning
• 12 Natural Gradient Learning and its Dynamics in Singular
• 13 Signal Processing and Optimization
• Index.