标题： 扩展的Sure独立筛选法ExSIS用于超高维线性模型 显示英文标题

标题： ExSIS: Extended Sure Independence Screening for Ultrahigh-dimensional Linear Models

摘要： 在超高维线性模型中，统计推断可能在计算上难以实现。基于相关性的变量筛选方法，即利用边缘相关性在统计推断之前从模型中移除无关变量，可以用来克服这一挑战。以往关于基于相关性的变量筛选的工作要么对线性模型施加统计先验，要么假设特定的筛选后推断方法。本文首先将基于相关性的变量筛选分析扩展到任意线性模型和筛选后的推断技术。 具体而言，(i) 它表明一个条件——称为筛选条件——对于成功地基于相关性筛选线性模型来说是充分的，并且(ii) 它提供了对基于边缘相关性筛选与不同问题参数之间依赖关系的见解。 数值实验确认了这些见解不仅仅是分析的产物；相反，它们反映了与基于边缘相关性变量筛选相关的挑战。 其次，本文明确推导了任意（随机或确定性）线性模型的筛选条件，在此过程中，它证明了——在适当条件下——即使活跃变量的数量几乎线性增长到样本大小时，也可以将超高维任意线性模型的维度减少到接近样本大小。 第三，它将筛选条件专门化为次高斯线性模型，并将最终结果与文献中现有的结果进行对比。 这种专门化正式验证了本文的主要结果概括了现有基于相关性的筛选结果的主张。 显示英文摘要

摘要： Statistical inference can be computationally prohibitive in ultrahigh-dimensional linear models. Correlation-based variable screening, in which one leverages marginal correlations for removal of irrelevant variables from the model prior to statistical inference, can be used to overcome this challenge. Prior works on correlation-based variable screening either impose statistical priors on the linear model or assume specific post-screening inference methods. This paper first extends the analysis of correlation-based variable screening to arbitrary linear models and post-screening inference techniques. In particular, (i) it shows that a condition---termed the screening condition---is sufficient for successful correlation-based screening of linear models, and (ii) it provides insights into the dependence of marginal correlation-based screening on different problem parameters. Numerical experiments confirm that these insights are not mere artifacts of analysis; rather, they are reflective of the challenges associated with marginal correlation-based variable screening. Second, the paper explicitly derives the screening condition for arbitrary (random or deterministic) linear models and, in the process, it establishes that---under appropriate conditions---it is possible to reduce the dimension of an ultrahigh-dimensional, arbitrary linear model to almost the sample size even when the number of active variables scales almost linearly with the sample size. Third, it specializes the screening condition to sub-Gaussian linear models and contrasts the final results to those existing in the literature. This specialization formally validates the claim that the main result of this paper generalizes existing ones on correlation-based screening.