Conditional variable screening via ordinary least squares projection

TL;DR

This paper introduces COLP, a variable screening method that leverages prior knowledge to improve accuracy in linear models, and an iterative extension FOLP that enhances performance with or without prior info.

Contribution

The paper proposes COLP and FOLP, novel methods that incorporate prior knowledge and iterative refinement for more effective variable screening in linear models.

Findings

COLP has the sure-screening property under certain conditions.

FOLP performs well even without prior knowledge, using a data-driven approach.

Simulation studies confirm the effectiveness of both methods.

Abstract

In this article, we propose a novel variable screening method for linear models named as conditional screening via ordinary least squares projection (COLP). COLP can take advantage of prior knowledge concerning certain active predictors by eliminating the adverse impact of their coefficients in the estimation of remaining ones and thus significantly enhance the screening accuracy. We prove its sure-screening property under reasonable assumptions and demonstrate its utility in an application to a leukemia dataset. Moreover, based on the conditional approach, we introduce an iterative algorithm named as forward screening via ordinary least squares projection (FOLP), which not only could exploit the prior information more effectively, but also has promising performance when no prior knowledge is available using a data-driven conditioning set. Extensive simulation studies are carried out to demonstrate the competence of both proposed methods.