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Feature Screening via Distance Correlation Learning

Author

Listed:
  • Runze Li
  • Wei Zhong
  • Liping Zhu

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.

Suggested Citation

  • Runze Li & Wei Zhong & Liping Zhu, 2012. "Feature Screening via Distance Correlation Learning," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1129-1139, September.
  • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:499:p:1129-1139
    DOI: 10.1080/01621459.2012.695654
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    3. Xiang-Jie Li & Xue-Jun Ma & Jing-Xiao Zhang, 2017. "Robust feature screening for varying coefficient models via quantile partial correlation," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(1), pages 17-49, January.
    4. Zhang, Jing & Liu, Yanyan & Wu, Yuanshan, 2017. "Correlation rank screening for ultrahigh-dimensional survival data," Computational Statistics & Data Analysis, Elsevier, vol. 108(C), pages 121-132.
    5. repec:spr:aistmt:v:70:y:2018:i:2:d:10.1007_s10463-016-0597-2 is not listed on IDEAS
    6. Huang, Qiming & Zhu, Yu, 2016. "Model-free sure screening via maximum correlation," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 89-106.
    7. Lai, Peng & Song, Fengli & Chen, Kaiwen & Liu, Zhi, 2017. "Model free feature screening with dependent variable in ultrahigh dimensional binary classification," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 141-148.
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    9. Yang, Hu & Guo, Chaohui & Lv, Jing, 2015. "SCAD penalized rank regression with a diverging number of parameters," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 321-333.
    10. repec:eee:jmvana:v:165:y:2018:i:c:p:1-13 is not listed on IDEAS
    11. repec:eee:ecolet:v:156:y:2017:i:c:p:162-167 is not listed on IDEAS
    12. Lan, Wei & Zhong, Ping-Shou & Li, Runze & Wang, Hansheng & Tsai, Chih-Ling, 2016. "Testing a single regression coefficient in high dimensional linear models," Journal of Econometrics, Elsevier, vol. 195(1), pages 154-168.
    13. repec:eee:csdana:v:122:y:2018:i:c:p:18-32 is not listed on IDEAS
    14. repec:eee:csdana:v:114:y:2017:i:c:p:88-104 is not listed on IDEAS
    15. Xin-Bing Kong & Zhi Liu & Yuan Yao & Wang Zhou, 2017. "Sure screening by ranking the canonical correlations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 46-70, March.
    16. repec:eee:stapro:v:126:y:2017:i:c:p:238-243 is not listed on IDEAS
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    18. repec:eee:csdana:v:119:y:2018:i:c:p:118-138 is not listed on IDEAS
    19. Li, Yujie & Li, Gaorong & Lian, Heng & Tong, Tiejun, 2017. "Profile forward regression screening for ultra-high dimensional semiparametric varying coefficient partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 133-150.
    20. Lin, Lu & Sun, Jing & Zhu, Lixing, 2013. "Nonparametric feature screening," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 162-174.
    21. Ma, Xuejun & Zhang, Jingxiao, 2016. "Robust model-free feature screening via quantile correlation," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 472-480.
    22. Lai, Peng & Liu, Yiming & Liu, Zhi & Wan, Yi, 2017. "Model free feature screening for ultrahigh dimensional data with responses missing at random," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 201-216.
    23. Peirong Xu & Lixing Zhu & Yi Li, 2014. "Ultrahigh dimensional time course feature selection," Biometrics, The International Biometric Society, vol. 70(2), pages 356-365, June.
    24. Sihai Dave Zhao & Yi Li, 2014. "Score test variable screening," Biometrics, The International Biometric Society, vol. 70(4), pages 862-871, December.

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