Feature Screening via Distance Correlation Learning

Abstract

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.

KEY WORDS:

• Sure independence screening
• Sure screening property
• Ultrahigh dimensionality
• Variable selection

Acknowledgments

Li's research was supported by a National Institute on Drug Abuse (NIDA) grant P50-DA10075 and a National Natural Science Foundation of China (NNSFC) grant 11028103. Zhong's research was supported by a NIDA grant P50-DA10075 as a graduate research assistant during his graduate study, and by an NNSFC grant 71131008 (Key Project). Zhu's research was supported by an NNSFC grant 11071077 and a NIDA grant R21-DA024260. All authors equally contributed to this article, and the authors are listed in the alphabetical order. The authors thank the editor, the associate editor, and reviewers for their constructive comments, which have led to a dramatic improvement in the earlier version of this article. The content is solely the responsibility of the authors and does not necessarily represent the official views of the NSF or NIDA.