Strong Sure Screening of Ultra-high Dimensional Data with Interaction Effects

TL;DR

This paper introduces a new interaction screening method for ultrahigh dimensional data that effectively detects interactions with strong effects but weak marginal signals, outperforming existing methods.

Contribution

A novel interaction screening procedure based on joint cumulants that achieves strong sure screening under realistic conditions.

Findings

The proposed method outperforms two existing interaction screening methods in simulations.

It successfully identifies interactions with strong effects and weak marginal signals.

Application to real data demonstrates its practical utility.

Abstract

Ultrahigh dimensional data sets are becoming increasingly prevalent in areas such as bioinformatics, medical imaging, and social network analysis. Sure independent screening of such data is commonly used to analyze such data. Nevertheless, few methods exist for screening for interactions among predictors. Moreover, extant interaction screening methods prove to be highly inaccurate when applied to data sets exhibiting strong interactive effects, but weak marginal effects, on the response. We propose a new interaction screening procedure based on joint cumulants which is not inhibited by such limitations. Under a collection of sensible conditions, we demonstrate that our interaction screening procedure has the strong sure screening property. Four simulations are used to investigate the performance of our method relative to two other interaction screening methods. We also apply a two-stage analysis to a real data example by first employing our proposed method, and then further examining a subset of selected covariates using multifactor dimensionality reduction.