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用于超高维无模型特征选择的边际切片逆回归AI 解读

Model-free variable selection has been implemented under the sufficient dimension reduction framework since the seminal paper of Cook [Ann. Statist. 32 (2004) 1062–1092]. In this paper, we extend the marginal coordinate test for sliced inverse regression (SIR) in Cook (2004) and propose a novel marginal SIR utility for the purpose of ultrahigh dimensional feature selection. Two distinct procedures, Dantzig selector and sparse precision matrix estimation, are incorporated to…

迹追踪：无模型变量选择的一般框架AI 解读

We propose trace pursuit for model-free variable selection under the sufficient dimension-reduction paradigm. Two distinct algorithms are proposed: stepwise trace pursuit and forward trace pursuit. Stepwise trace pursuit achieves selection consistency with fixed p. Forward trace pursuit can serve as an initial screening step to speed up the computation in the case of ultrahigh dimensionality. The screening consistency property of forward trace pursuit based on sliced inverse…

非椭圆分布预测变量的降维AI 解读

Sufficient dimension reduction methods often require stringent conditions on the joint distribution of the predictor, or, when such conditions are not satisfied, rely on marginal transformation or reweighting to fulfill them approximately. For example, a typical dimension reduction method would require the predictor to have elliptical or even multivariate normal distribution. In this paper, we reformulate the commonly used dimension reduction methods, via the notion of…