标题： 超高维变量选择：超越线性模型 显示英文标题

标题： Ultrahigh dimensional variable selection: beyond the linear model

摘要： 高维空间中的变量选择表征了许多当代科学发现和决策制定中的问题。 许多常用的技术基于独立性筛选；举例来说，包括相关性排名（Fan 和 Lv，2008）或者使用两样本t检验的高维分类特征选择（Tibshirani 等人，2003）。 在线性模型的背景下，Fan 和 Lv（2008）表明，在某些条件下，这种简单的相关性排名具有确定性的独立筛选属性，并且当特征边缘上无关但联合与响应变量相关时，需要对其进行修订，称为迭代确定性独立筛选（ISIS）。 本文中，我们在不显式定义残差的情况下，将ISIS扩展到一个通用的伪似然框架中，该框架包括广义线性模型作为特殊情况。 即使在最小二乘设定下，新方法通过允许在迭代过程中删除变量来改进ISIS。 我们的技术使我们能够在高维分类中选择重要的特征，而常用的两样本t方法失败。 引入了一种新技术以减少特征筛选阶段的错误发现率。 提出了几个模拟例子和两个真实数据例子来说明该方法论。 显示英文摘要

摘要： Variable selection in high-dimensional space characterizes many contemporary problems in scientific discovery and decision making. Many frequently-used techniques are based on independence screening; examples include correlation ranking (Fan and Lv, 2008) or feature selection using a two-sample t-test in high-dimensional classification (Tibshirani et al., 2003). Within the context of the linear model, Fan and Lv (2008)showed that this simple correlation ranking possesses a sure independence screening property under certain conditions and that its revision, called iteratively sure independent screening (ISIS), is needed when the features are marginally unrelated but jointly related to the response variable. In this paper, we extend ISIS, without explicit definition of residuals, to a general pseudo-likelihood framework, which includes generalized linear models as a special case. Even in the least-squares setting, the new method improves ISIS by allowing variable deletion in the iterative process. Our technique allows us to select important features in high-dimensional classification where the popularly used two-sample t-method fails. A new technique is introduced to reduce the false discovery rate in the feature screening stage. Several simulated and two real data examples are presented to illustrate the methodology.