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<p>In this paper, we propose a novel model-free feature screening procedure via Grothendieck’s correlation for ultrahigh-dimensional data. Since Grothendieck’s correlation does not need moment restrictions on random vectors and the influence function of Grothendieck’s covariance is bounded, the proposed feature screening method is robust to heavy-tailed distributions or outliers. Furthermore, we select the threshold by using the reflection via data splitting method to control the false discovery rate at a pre-specified level. Meanwhile, the proposed algorithm for screening active features is highly efficient due to the low complexity of estimating the Grothendieck’s correlation. In addition, the proposed feature screening procedure enjoys both the sure screening property and FDR control simultaneously under certain technical conditions. Finally, we illustrate the satisfactory finite sample performance of our feature screening method via extensive numerical simulations and a real dataset analysis.</p>

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Robust feature screening via Grothendieck’s correlation with FDR control

  • 期刊论文

  • 发表日期：

    2025年7月3日

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  • Yunlu Jiang,
  • Xiaowen Huang,
  • Jing Tan,
  • Ruizhe Jiang

摘要

In this paper, we propose a novel model-free feature screening procedure via Grothendieck’s correlation for ultrahigh-dimensional data. Since Grothendieck’s correlation does not need moment restrictions on random vectors and the influence function of Grothendieck’s covariance is bounded, the proposed feature screening method is robust to heavy-tailed distributions or outliers. Furthermore, we select the threshold by using the reflection via data splitting method to control the false discovery rate at a pre-specified level. Meanwhile, the proposed algorithm for screening active features is highly efficient due to the low complexity of estimating the Grothendieck’s correlation. In addition, the proposed feature screening procedure enjoys both the sure screening property and FDR control simultaneously under certain technical conditions. Finally, we illustrate the satisfactory finite sample performance of our feature screening method via extensive numerical simulations and a real dataset analysis.