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活动类型：学术报告

主讲人：Jun Zhang

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活动内容：

 

Information Geometry

- the Differential Geometric Study of the

Manifold of Probability Density Functions

Jun Zhang  (University of Michigan-Ann Arbor)

 

Let M be a Riemannian manifold with a semi-positive metric g and a torsion-free connection $\nabla$. When $\nabla g$ is totally symmetric, one can introduce another torsion-free connection (uniquely) that is dual/conjugate to $\nabla$ with respect to g. The resulting geometry, which was investigated in the affine hypersurface theory by affine geometers, has recently found applications in theoretical statistics. There, M is called a "statistical manifold", modeling a parametric family of probability density functions. This seminar will introduce to geometers the background as well as recent results in information geometry. Of special interest is the notion of “divergence functions” (e.g. Kullback-Leibler diveregence, Bregman divergence as used in machine learning and statistics) and their connection to the geometric structure, which reveal representation and reference biduality.   

张老师希望在这里招到学生或者博士后，有兴趣的人不要错过