财大数统学院
下载中心
讲座 您现在所在的位置: 首页资源分类讲座

金邦梯教授讲座公告
来源:中南财经政法大学统计与数学学院    编辑:佚名    时间:2017-5-8    点击数:

  人:金邦梯(伦敦大学学院)

报告时间:5月16号上午9:00—9:40

报告地点:文波楼4楼会议室

报告题目:Variational Gaussian Approximation for Poisson Data

   要:The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to a numerically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation for approximating the posterior distribution arising from the Poisson model with a Gaussian prior. This is achieved by seeking an optimal Gaussian distribution minimizing the Kullback-Leibler divergence, or equivalently maximizing the lower bound for the model evidence. We shall derive an explicit expression for the lower bound, and establish the existence and uniqueness of the optimal Gaussian approximation. The lower bound functional can be viewed as a variant of classical Tikhonov regularization, but penalizing also the covariance of the estimate, instead of only the mean. We develop an efficient alternating direction maximization algorithm for solving the problem, and discuss the strategies for reducing the computational complexity via low rank structure of the forward operator and the sparsity of the covariance. Further, as an illustration of the use of the lower bound, we discuss the hierarchical Bayesian modeling for automatically selecting the hyperparameter in the prior distribution, and propose a monotonically convergent algorithm for determining the hyperparameter. We present extensive numerical experiments to illustrate the Gaussian approximation and the algorithms.

主讲人简介:

金邦梯,2008年获香港中文大学数学博士学位。20091月至20108月在德国布莱梅工业数学中心做博士后,20109月至20138月在美国德州农工大学应用和计算数学研究所做访问助理教授, 20139月至20148月受聘于美国加州大学河边分校数学系助理教授 20149月至今受聘于英国伦敦大学学院(TIMES/QS排名全球前10)计算机科学系(终身职位)。金邦梯教授主要研究领域涉及反问题建模计算,分数阶偏微分方程正反问题的理论与计算,统计计算等;获得Inverse Problems Young Researcher Award (2014), MediaV Young Researcher Award (2012) 出版专著Inverse Problems: Tikhonov Theory and Algorithms一部,在国际顶级学术刊物 SIAM系列, Inverse Problem, Journal of Computational Physics, Mathematics of Computation, Applied and Computational Harmonic Analysis, IEEE T. Signal Processing 等发表论文70余篇,Google Scholar 总引次数2000余次,担任 Fractional Calculus and Applied Analysis编委,并担任Guest editor for special issue of Inverse Problems。