Southwest Jiaotong University School of Mathematics


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ag网站亚游登录:   作者:郑海涛     日期:2014-06-24 00:00:00   点击数:  



讲座题目$l_q$-Aggregation and Adaptive High-dimensional

                       Minimax Estimation

报告人:   Yang,Yuhong教授,明尼苏达大学统计学院

主持人:    殷向荣教授
讲座时间:  2014年6月27日上午10:00

讲座地点:  犀浦校区二号教学楼X2511

内容简介:Given a dictionary of M initial regression functions and n observations of (X, Y), we seek to achieve the performance of the best linear combination of the M functions with the coefficients satisfying a sparsity constraint: the $l_q$ norm of the coefficients, with q between 0 and 1, is upper bounded by some constant t>0. This problem is called the $l_q$-aggregation of estimates, which turns out to include the previously well understood different types of aggregation problems. Here no specific assumption between M and n is made.

     To solve the general $l_q$-aggregation problem, we first establish a sharp high-dimensional sparse linear approximation bound without any assumption on the relationship between the M initial functions. Together with general model selection/mixing results, we show that our final estimators adaptively achieve the minimax rate of convergence for $l_q$-aggregation simultaneously for all q in [0, 1] and t>0. Implications on adaptive high-dimensional linear regression in $l_q$-hulls will be given as well.



      Yang,Yuhong,明尼苏达大学统计学院教授,博士毕业于美国耶鲁大学,现任国际统计杂志Annals of Institute of Statistical Mathematics和Statistics Surveys副主编,Institute of Mathematical Statistics Fellow。 在Ann. Statist.、JASA、JRSSB, JSPI等国外顶尖期刊发表学术论文四十余篇。




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