Linear screening for high-dimensional computer experiments

TL;DR

This paper introduces a simple linear variable screening method for high-dimensional computer experiments, effective when the number of variables exceeds the number of runs, and demonstrates its theoretical validity and superior performance.

Contribution

It proposes a novel linear screening approach for high-dimensional settings and a two-stage procedure to enhance accuracy, applicable when the underlying model is nearly sparse.

Findings

Method outperforms existing model-free screening techniques.

Proven asymptotic validity under mild conditions.

Two-stage approach improves screening accuracy.

Abstract

In this paper we propose a linear variable screening method for computer experiments when the number of input variables is larger than the number of runs. This method uses a linear model to model the nonlinear data, and screens the important variables by existing screening methods for linear models. When the underlying simulator is nearly sparse, we prove that the linear screening method is asymptotically valid under mild conditions. To improve the screening accuracy, we also provide a two-stage procedure that uses different basis functions in the linear model. The proposed methods are very simple and easy to implement. Numerical results indicate that our methods outperform existing model-free screening methods.