| Title: | Referential Duality and Representational Duality in Information Geometry |
| Date: |
April 2, 2007 (Monday)
|
| Time: |
4:30 p.m. - 5:30 p.m.
|
| Venue: |
Room 1027, 10/F, Ho Sin-hang Engineering Building,
The Chinese University of Hong Kong, Shatin, N.T. |
| Speaker: |
Dr. Jun Zhang
Department of Psychology University of Michigan, Ann Arbor USA |
Information geometry investigates differential geometry of the manifold of non-parametric or parametric probability density functions, i.e., the space of statistical models. Central to this framework is the notion of "divergence function", which measures (not necessarily symmetric) difference between two density functions (points on the manifold). Examples include f-divergence, alpha-divergence, Jensen difference, etc, which all include Kullback-Leibler divergence as a special case and all induce the same geometric structure, the so-called "statistical manifold", with Fisher information as the Riemannian metric and alpha-connection as a family of affine connections. In this talk, I will present a general method of constructing divergence functions based on convex analysis. I will then draw a clear distinction between two senses of duality on a statistical manifold, namely, "referential duality" regarding the effect of assignment, in the divergence function, reference/comparison status of the two (probability density) functions, and "representational duality" regarding the effect of a monotonic transformation of these functions on the induced Riemannian structure (metric and conjugate connections). Its implication to machine learning will be discussed.
BIOGRAPHY:
Dr. Zhang received the B.Sc. degree in Theoretical Physics from Fudan University in 1985, and Ph.D. degree in Neuroscience from University of California, Berkeley in 1992. Supported by a McDonnel-Pew Postdoctoral Fellowship, he worked at the Computation Neuroscience Laboratory headed by Terrance Sejnowski at the Salk Institute. He then joined the faculty of the University of Michigan, Department of Psychology, as Assistant Professor, Associate Professor, and Full Professor starting September 2007. He has also held visiting positions as Senior Lecturer, Associate Professor, and Research Scientist at the University of Melbourne, the University of Waterloo, and RIKEN Brain Science Institute, respectively. In 2003, he was selected to deliver the Winer Memorial Serial Lectures at the Department of Psychology, Purdue University. He has published two dozens of peer-reviewed journal papers in the field of vision, mathematical psychology, cognitive psychology, game theory, voting theory, etc. Dr. Zhang serves as an Associate Editor for the Journal of Mathematical Psychology and is an elected member of the Governing Board of the Society for Mathematical Psychology. In the past, he has organized or co-organized several international conferences and workshops in mathematical psychology and information geometry. His research is funded by the National Science Foundation (NSF) and Air Force Office for Scientific Research (AFOSR).
Enquiries: Prof. Lei Xu at tel 2609 8423
For more information, please refer to http://www.cse.cuhk.edu.hk/seminar