活动地点：

活动类型：学术报告

主讲人：Jun Zhang

活动时间：

活动内容：

Three Lectures on Information Geometry

 

Prof. Jun Zhang (University of Michigan Ann Arbor)

 

Lecture Time: August 24(Fri), 27(Mon), 29(Wed)

 

Location: CMS

 

Information geometry, narrowly speaking, is the differential geometric study of the manifold of probability density functions (or probability distributions on discrete support). From a geometric perspective, a parametric family of probability density functions on a sample space is modeledas a differentiable manifold, where points on the manifold represent the density functions themselves and coordinates represent the indexing parameters. Information Geometry is seen as an emerging tool for providing a unified perspective to many branches of information science, including coding, statistics, machine learning, inference and decision, etc.

 

In three2-hour lectures, I will provide an in-depth introduction to basic concepts of information geometry and its relation to affine differential geometry.Topics include:Kullback-Leibler divergence and Bregman divergence, Fisher-Rao metric, conjugate (dual) connections, alpha-connections, statistical manifold, curvature, dually-flat manifold, exponential family, natural parameter/expectation parameter, affine immersion,equiaffine geometry,centro-affine immersion, alpha-Hessian manifold, projective and conformal equivalence, symplectic, Kahler, and Einstein-Weyl structures, etc.

 

MATERIALS:

S. Amari and H. Nagaoka (2000).Method of Information Geometry. AMS monograph vol 191. Oxford University Press.

U. Simon, A. Schwenk-Schellschmidt, and H. Viesel. (1991). Introduction to the Affine Differential Geometry of Hypersurfaces.Science University of Tokyo Press.

Zhang, J. (2004). Divergence function, duality, and convex analysis.Neural Computation, vol16, 159-195.