Information Geometry: Introduction and Advanced Topics
Student No.:25
Time:Wed & Thu 09:50-11:25, Jul.11/12/18/19
Instructor:张俊 Zhang Jun  
Place:Conference Room 3 (Wed, Jul.11/18), Conference Room 2 (Thu, Jul.12/19), Jin Chun Yuan West Bldg.
Starting Date:2018-7-11
Ending Date:2018-7-19

This 8-lecture series will introduce the audience to fundamental materials of information geometry. Information Geometry is the differential geometric study of the manifold of parametric (and recently, non-parametric) probability models. It is build upon a Riemannian geometric structure with Fisher-Rao metric and Amari-Censov tensor, which are related to generally non-symmetric “distance” functions on such manifolds. It provides a geometric foundation for many applied disciplines such as inferential (including Bayesian) statistics, machine learning, information and coding theory, computation neuroscience, etc. After a thorough introduction, the course will focus on geometric structures revealed on such manifolds: statistical structure, Codazzi coupling, Kahler and para-Kahler structure, Codazzi-(para)-Kahler structure, symplectic connections, complex connections, holomorphic connections, etc.

Prerequisite: The course is open to students with a variety of backgrounds:
1) For mathematics students: Differential Geometry
2) For statistics students: Point Estimation Theory
3) For machine learning students: Convex Analysis

Reference: S. Amari and H. Nagaoka (2000). Methods of Information Geometry, AMS monograph