On Exact Feature Screening in Ultrahigh-Dimensional Binary Classification

Abstract

We propose a new model-free feature screening method based on energy distances for ultrahigh-dimensional binary classification problems. With a high probability, the proposed method retains only relevant features after discarding all the noise variables. The proposed screening method is also extended to identify pairs of variables that are marginally undetectable but have differences in their joint distributions. Finally, we build a classifier that maintains coherence between the proposed feature selection criteria and discrimination method, and also establish its risk consistency. An extensive numerical study with simulated and real benchmark datasets shows clear and convincing advantages of our proposed method over the state-of-the-art methods. Supplementary materials for this article are available online.

KEYWORDS:

• Energy distances
• Exponential bound
• Non-bipartite matching
• Paired features
• Ratio of order statistics
• Scale-adjusted average distances

Supplementary Materials

All proofs and mathematical details are provided in the Supplementary material available online. The Supplementary also contains algorithms of the proposed screening methods and some additional numerical results.

Acknowledgments

The authors would like to thank the Editor, Associate Editor and two anonymous reviewers for their careful reading of the manuscript and thoughtful comments.

Disclosure Statement

The authors report there are no competing interests to declare.

Additional information

Funding

The research of the second author was partially supported by the INSPIRE Faculty Fellowship from the Department of Science and Technology, Government of India.