Model-Free Forward Screening Via Cumulative Divergence

Abstract

Feature screening plays an important role in the analysis of ultrahigh dimensional data. Due to complicated model structure and high noise level, existing screening methods often suffer from model misspecification and the presence of outliers. To address these issues, we introduce a new metric named cumulative divergence (CD), and develop a CD-based forward screening procedure. This forward screening method is model-free and resistant to the presence of outliers in the response. It also incorporates the joint effects among covariates into the screening process. With a data-driven threshold, the new method can automatically determine the number of features that should be retained after screening. These merits make the CD-based screening very appealing in practice. Under certain regularity conditions, we show that the proposed method possesses sure screening property. The performance of our proposal is illustrated through simulations and a real data example. Supplementary materials for this article are available online.

Keywords:

• Cumulative divergence
• Feature screening
• Forward screening
• High dimensionality
• Sure screening property
• Variable selection

Acknowledgments

The authors thank the AE, and the reviewers for their constructive comments, which have led to a significant improvement of the earlier version of this article. Liping Zhu is the corresponding author.

Supplementary Materials

The supplementary material contains the proofs of Statement (2.2), Lemma 2, Proposition 1 and Theorem 1.

Additional information

Funding

This work was supported by National Natural Science Foundation of China (NNSFC) grants 11731011, 11690014, 11690015, 11731011 and 11801501, NSERC RGPIN-2016-05024, NSF grant DMS 1820702 and NIDA, NIH grant P50 DA039838, the Ministry of Education Project of Key Research Institute of Humanities and Social Sciences at Universities (16JJD910002) and National Youth Top-notch Talent Support Program, P. R. China. The content is solely the responsibility of the authors and does not necessarily represent the official views of NNSFC, MEC, NSF, NIH or NIDA