Feature Screening via Distance Correlation Learning

Runze Li Penn State University Wei Zhong Xiamen University Liping Zhu Renmin University

Statistics Theory and Methods mathscidoc:1702.33002

Journal of American Statistical Association, 107, (499), 1129, 2012.9
This article 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). The DC-SIS can be implemented as easily as the sure independence screening (SIS) procedure based on the Pearson correlation proposed by Fan and Lv. However, the DC-SIS can significantly improve the SIS. Fan and Lv 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 multivariate response variables. We establish the sure screening property for the DC-SIS, and conduct simulations to examine its finite sample performance. A 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.
Sure independence screening; Sure screening property; Ultrahigh dimensionality; Variable selection
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  title={Feature Screening via Distance Correlation Learning},
  author={Runze Li, Wei Zhong, and Liping Zhu},
  booktitle={Journal of American Statistical Association},
Runze Li, Wei Zhong, and Liping Zhu. Feature Screening via Distance Correlation Learning. 2012. Vol. 107. In Journal of American Statistical Association. pp.1129. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170205112114593743157.
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