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講座題目：$l_q$-Aggregation and Adaptive High-dimensional

                       Minimax Estimation

報(bào)告人：   Yang，Yuhong教授，明尼蘇達(dá)大學(xué)統(tǒng)計(jì)學(xué)院

主持人：    殷向榮教授
講座時(shí)間：  2014年6月27日上午10:00

講座地點(diǎn)：  犀浦校區(qū)二號(hào)教學(xué)樓X2511

內(nèi)容簡(jiǎn)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.

主講人簡(jiǎn)介：

      Yang，Yuhong，明尼蘇達(dá)大學(xué)統(tǒng)計(jì)學(xué)院教授，博士畢業(yè)于美國(guó)耶魯大學(xué)，現(xiàn)任國(guó)際統(tǒng)計(jì)雜志Annals of Institute of Statistical Mathematics和Statistics Surveys副主編，Institute of Mathematical Statistics Fellow。 在Ann. Statist.、JASA、JRSSB, JSPI等國(guó)外頂尖期刊發(fā)表學(xué)術(shù)論文四十余篇。

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