ExSIS: Extended sure independence screening for ultrahigh-dimensional linear models
ExSIS: Extended sure independence screening for ultrahigh-dimensional linear models
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DOI：
10.1016/j.sigpro.2019.01.018
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发表时间：
2019-06-01
影响因子：
4.4
通讯作者：
Bajwa, Waheed U.
中科院分区：
文献类型：
--
作者：
Ahmed, Talal;Bajwa, Waheed U.
在超高维线性模型中，统计推断可能在计算上是禁止的。基于相关性的变量筛选可以用来克服这一挑战，在这种筛选中，人们利用边际相关性在统计推断之前从模型中去除不相关的变量。基于相关性的变量筛选的先前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理方法。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推理技术。特别是，（i）它表明，一个条件，被称为筛选条件，是足够的成功的相关性为基础的筛选线性模型，（ii）它提供了深入的了解依赖于不同的问题参数的边际相关性为基础的筛选。数值实验证实，这些见解不仅仅是分析的文物，相反，它们反映了与基于边际相关性的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，并在此过程中，它建立了在适当的条件下，即使当活动变量的数量几乎与样本大小成线性关系时，也可以将超高维任意线性模型的维数降低到几乎样本大小。第三，它专门的筛选条件，以亚高斯线性模型和对比的最终结果，现有的文献。这种专业化正式验证了本文的主要结果概括了现有的基于相关性的筛选。(C)2019 Elsevier B.V.版权所有。
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. (C) 2019 Elsevier B.V. All rights reserved.