Aggregated Sure Independence Screening for Variable Selection with Interaction Structures

TL;DR

This paper introduces an aggregated sure independence screening method that efficiently handles variable selection with interactions in ultra-high-dimensional data, overcoming computational barriers and including important interactions regardless of main effect strength.

Contribution

The proposed method addresses computational challenges in high-dimensional interaction variable selection, enabling inclusion of important interactions even with weak or absent main effects.

Findings

Efficiently handles ultra-high-dimensional data with p >> n.

Includes important interactions regardless of main effect strength.

Compatible with arbitrary variable selection methods.

Abstract

A new method called the aggregated sure independence screening is proposed for the computational challenges in variable selection of interactions when the number of explanatory variables is much higher than the number of observations (i.e., $p\gg n$). In this problem, the two main challenges are the strong hierarchical restriction and the number of candidates for the main effects and interactions. If $n$ is a few hundred and $p$ is ten thousand, then the memory needed for the augmented matrix of the full model is more than $100{\rm GB}$ in size, beyond the memory capacity of a personal computer. This issue can be solved by our proposed method but not by our competitors. Two advantages are that the proposed method can include important interactions even if the related main effects are weak or absent, and it can be combined with an arbitrary variable selection method for interactions. The research addresses the main concern for variable selection of interactions because it makes previous methods applicable to the case when $p$ is extremely large.