An ensemble learning method for variable selection: application to high dimensional data and missing values

TL;DR

This paper introduces an ensemble learning-based variable selection method tailored for high-dimensional and incomplete data, demonstrating improved accuracy and error control over existing methods through simulations and real data applications.

Contribution

It proposes a novel ensemble variable selection approach that effectively handles high-dimensional data with missing values, extending classical methods and providing theoretical and empirical validation.

Findings

Improves error risk control, especially type I error, in low-dimensional settings.

Performs better than multiple imputation-based methods with missing data.

Achieves similar high-dimensional performance with or without missing data.

Abstract

Standard approaches for variable selection in linear models are not tailored to deal properly with high-dimensional and incomplete data. Currently, methods dedicated to high-dimensional data handle missing values by ad-hoc strategies, like complete case analysis or single imputation, while methods dedicated to missing values, mainly based on multiple imputation, do not discuss the imputation method to use with high-dimensional data. Consequently, both approaches appear to be limited for many modern applications. With inspiration from ensemble methods, a new variable selection method is proposed. It extends classical variable selection methods in the case of high-dimensional data with or without missing data. Theoretical properties are studied and the practical interest is demonstrated through a simulation study, as well as through an application to models specification in sequential multiple imputation. In the low dimensional case, the procedure improves the control of the error risks, especially type I error, even without missing values for stepwise, lasso or knockoff methods. With missing values, the method performs better than reference selection methods based on multiple imputation. Similar performances are obtained in the high-dimensional case with or without missing values.