ABSTRACT Conditional variable screening arises when researchers have prior information regarding the importance of certain predictors. It is natural to consider feature screening methods conditioning on these known important predictors. Barut, E., Fan, J., and Verhasselt, A. [(2016), ‘Conditional Sure Independence Screening’, Journal of the American Statistical Association, 111, 1266–1277] proposed conditional sure independence screening (CSIS) to address this issue under the context of generalised linear models. While CSIS outperforms the marginal screening method when few of the factors are known to be important and/or significant correlations between some of the factors exist, unfortunately, CSIS is model based and might fail when the models are misspecified. We propose a model-free conditional screening method under the framework of sufficient dimension reduction for ultrahigh dimensional statistical problems. Numerical studies show our method easily beats CSIS for nonlinear models and performs comparable to CSIS for (generalised) linear models. Sure screening consistency property for our method is proved.

中文翻译：

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通过充分降维的无模型条件筛选方法

摘要 当研究人员获得有关某些预测因子重要性的先验信息时，就会出现条件变量筛选。考虑以这些已知的重要预测因子为条件的特征筛选方法是很自然的。Barut, E.、Fan, J. 和 Verhasselt, A. [(2016), 'Conditional Sure Independence Screening', Journal of the American Statistical Association, 111, 1266–1277] 提出了条件确定独立筛选 (CSIS) 来解决广义线性模型背景下的这个问题。虽然当已知的重要因素很少和/或某些因素之间存在显着相关性时，CSIS 优于边际筛选方法，但不幸的是，CSIS 是基于模型的，并且在错误指定模型时可能会失败。针对超高维统计问题，我们在充分降维的框架下提出了一种无模型条件筛选方法。数值研究表明，我们的方法在非线性模型方面很容易击败 CSIS，并且在（广义）线性模型方面的表现可与 CSIS 相媲美。证明了我们方法的确定筛选一致性属性。