Information Geometry: Introduction and Advanced Topics
Student No.:50
Time:Mon/Tue/Fri 9:50-11:25, 2017-07-31~2017-08-11
Instructor:Jun Zhang  [University of Michigan Ann Arbor]
Place:Mon/Fri: Conference Room 3; Tue: Conference Room 1
Starting Date:2017-7-31
Ending Date:2017-8-11



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.  





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






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