西南交通大学“创源”大讲堂研究生学术讲座
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.
主讲人简介：
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。
主办：研究生院
承办：数学学院
