Abstract

Variable screening methods have been shown to be effective in dimension reduction under the ultra-high dimensional setting. Most existing screening methods are designed to rank the predictors according to their individual contributions to the response. As a result, variables that are marginally independent but jointly dependent with the response could be missed. In this work, we propose a new framework for variable screening, random subspace ensemble (RaSE), which works by evaluating the quality of random subspaces that may cover multiple predictors. This new screening framework can be naturally combined with any subspace evaluation criterion, which leads to an array of screening methods. The framework is capable to identify signals with no marginal effect or with high-order interaction effects. It is shown to enjoy the sure screening property and rank consistency. We also develop an iterative version of RaSE screening with theoretical support. Extensive simulation studies and real-data analysis show the effectiveness of the new screening framework.

摘要

变量筛选方法已被证明在超高维设置下对降维有效。大多数现有筛选方法旨在根据预测变量对响应的各自贡献对预测变量进行排名。因此，可能会遗漏边际独立但与响应共同依赖的变量。在这项工作中，我们提出了一个新的变量筛选框架，随机子空间集成 (RaSE)，它通过评估可能覆盖多个预测变量的随机子空间的质量来工作。这种新的筛选框架可以自然地与任何子空间评估标准结合，从而产生一系列筛选方法。该框架能够识别没有边际效应或具有高阶交互效应的信号。它显示出具有确定的筛选属性和等级一致性。我们还开发了具有理论支持的 RaSE 筛选的迭代版本。广泛的模拟研究和真实数据分析显示了新筛选框架的有效性。