Classification with Ultrahigh-Dimensional Features

TL;DR

This paper presents a new computationally feasible method for classification in ultrahigh-dimensional data, effectively detecting weak signals and recovering true features, with proven asymptotic optimality and superior discovery boundaries.

Contribution

Introduces a novel multivariate screening and classification method that leverages inter-feature correlations for ultrahigh-dimensional data, improving detection and recovery of informative features.

Findings

Achieves asymptotic optimal misclassification rates.

Provides more powerful discovery boundaries than previous methods.

Demonstrates effectiveness through simulations and real patient data classification.

Abstract

Although much progress has been made in classification with high-dimensional features \citep{Fan_Fan:2008, JGuo:2010, CaiSun:2014, PRXu:2014}, classification with ultrahigh-dimensional features, wherein the features much outnumber the sample size, defies most existing work. This paper introduces a novel and computationally feasible multivariate screening and classification method for ultrahigh-dimensional data. Leveraging inter-feature correlations, the proposed method enables detection of marginally weak and sparse signals and recovery of the true informative feature set, and achieves asymptotic optimal misclassification rates. We also show that the proposed procedure provides more powerful discovery boundaries compared to those in \citet{CaiSun:2014} and \citet{JJin:2009}. The performance of the proposed procedure is evaluated using simulation studies and demonstrated via classification of patients with different post-transplantation renal functional types.