Feature Screening via Distance Correlation Learning
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基于距离相关学习的特征筛选
- 研究问题
- 在超高维数据中，如何在不预先指定响应与预测变量模型的情况下筛选特征，并处理分组变量与多元响应？
- 方法与思路
- 作者提出基于距离相关的确定独立筛选程序DC-SIS，建立确定筛选性质，并通过模拟和真实数据与Pearson相关筛选比较。
- 材料陈述的贡献
- 摘要称DC-SIS的确定筛选性质适用于比线性模型更一般的情形，支持分组预测变量和多元响应，数值比较显示改善。
- 阅读关注点
- 应核对确定筛选所需的信号与维度条件、边际筛选对联合相关结构的限制，以及模拟比较的模型和调参规则。
- 阅读边界
- 仅据版本未注明的OpenAlex摘要，更一般情形的具体范围未说明；所述数值优势不能视为所有高维模型中的普遍优势。
原文摘要
This paper is concerned with screening features in ultrahigh dimensional data analysis, which has become increasingly important in diverse scientific fields. We develop a sure independence screening procedure based on the distance correlation (DC-SIS, for short). The DC-SIS can be implemented as easily as the sure independence screening procedure based on the Pearson correlation (SIS, for short) proposed by Fan and Lv (2008). However, the DC-SIS can significantly improve the SIS. Fan and Lv (2008) established the sure screening property for the SIS based on linear models, but the sure screening property is valid for the DC-SIS under more general settings including linear models. Furthermore, the implementation of the DC-SIS does not require model specification (e.g., linear model or generalized linear model) for responses or predictors. This is a very appealing property in ultrahigh dimensional data analysis. Moreover, the DC-SIS can be used directly to screen grouped predictor variables and for multivariate response variables. We establish the sure screening property for the DC-SIS, and conduct simulations to examine its finite sample performance. Numerical comparison indicates that the DC-SIS performs much better than the SIS in various models. We also illustrate the DC-SIS through a real data example.