Fw: 实验室统计中心学术报告，05月24日（周四） 15:30-16:30，N620
z...@amss.ac.cn
主题: 实验室统计中心学术报告，05月24日（周四） 15:30-16:30，N620
中科院随机复杂结构与数据科学重点实验室
中科院数学与系统科学研究院
统计科学研究中心
学术报告
题 目: Hi-dimensional Variable Selection for Nonlinear Models
报 告 人: Jun Liu
Department of Statistics, Harvard University
时 间： 2018年05月24日（周四） 15:30-16:30
地 点： 数学院南楼620
摘 要： We consider multiple index models, in which the response Ydepends on the p-dimensional predictor vector X=(X_1,…,X_p ) only through a few linear combinations, i.e., Y=f(β_1^T X,…,β_d^T X,ϵ), where the link function f( ) is unknown. The space spanned by β_1,…,β_d is called the sufficient dimension reduction (SDR) space. When p is very large, we are interested in both estimating the SDR space and also conducting variable selection under certain sparsity assumption. We found a way to use the Lasso linear regression algorithm to efficiently estimate of the SDR subspace. This algorithm, Lasso-SIR, is shown to be consistent and to achieve the optimal convergence rate under certain sparsity conditions when p is of order o(n^2 λ^2), where λ is the generalized signal-noise ratio.
From an algorithmic point of view, SIR is closely related to the linear discriminant analysis (LDA) for classification problems. Thus, variable selections for index models can also be formulated as a variable selection for LDA or QDA. We propose a forward-backward method, SODA, for variable selection with both main and quadratic interaction terms under the logistic regression framework. SODA can deal with high-dimensional data with the number of predictors much larger than the sample size and does not require the joint normality assumption on predictors, or the linearity and constant variance conditions employed in the SIR literature, leading to much enhanced robustness. Our simulation studies as well as real-data applications demonstrate superior performances of SODA in dealing with non-Gaussian design matrices in both logistic and general index models. Some open theoretical issues remain.
邀请人：孙六全
JH Zhang
张老师，
好的，谢谢您，有时间向您请教。
祝好！
张俊华
-----原始邮件-----
发件人:z...@amss.ac.cn
发送时间:2018-05-17 11:21:58 (星期四)
收件人: zhangroup-seminar <zhangrou...@googlegroups.com>
抄送:
主题: [ZHANGroup-seminar] Fw: 实验室统计中心学术报告，05月24日（周四） 15:30-16:30，N620
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JH Zhang
不好意思，刚才这个邮件发错了，抱歉！
祝好！
俊华
-----原始邮件-----
发件人:"JH Zhang" <z...@amt.ac.cn>
发送时间:2018-05-20 12:39:08 (星期日)
收件人: zhangrou...@googlegroups.com
抄送:
主题: Re: [ZHANGroup-seminar] Fw: 实验室统计中心学术报告，05月24日（周四） 15:30-16:30，N620