Conditional Sure Independence Screening

TL;DR

This paper introduces Conditional Sure Independence Screening (CSIS) for variable selection in ultrahigh-dimensional generalized linear models, improving accuracy by incorporating prior knowledge and reducing false positives and negatives.

Contribution

The paper develops CSIS, a novel method that leverages prior information to enhance variable screening accuracy in high-dimensional settings, with theoretical guarantees and practical algorithms.

Findings

CSIS reduces false positive and false negative rates.

Theoretical conditions for sure screening and model selection consistency.

Demonstrated effectiveness through simulations and real data analysis.

Abstract

Independence screening is a powerful method for variable selection for `Big Data' when the number of variables is massive. Commonly used independence screening methods are based on marginal correlations or variations of it. In many applications, researchers often have some prior knowledge that a certain set of variables is related to the response. In such a situation, a natural assessment on the relative importance of the other predictors is the conditional contributions of the individual predictors in presence of the known set of variables. This results in conditional sure independence screening (CSIS). Conditioning helps for reducing the false positive and the false negative rates in the variable selection process. In this paper, we propose and study CSIS in the context of generalized linear models. For ultrahigh-dimensional statistical problems, we give conditions under which sure screening is possible and derive an upper bound on the number of selected variables. We also spell out the situation under which CSIS yields model selection consistency. Moreover, we provide two data-driven methods to select the thresholding parameter of conditional screening. The utility of the procedure is illustrated by simulation studies and analysis of two real data sets.