Ultrahigh dimensional variable selection: beyond the linear model

TL;DR

This paper extends iterative sure independence screening (ISIS) to a broader pseudo-likelihood framework, improving variable selection in high-dimensional data, especially for classification tasks where traditional methods fail, and introduces techniques to reduce false discoveries.

Contribution

It generalizes ISIS beyond linear models to a pseudo-likelihood framework, enabling better feature selection and false discovery control in high-dimensional settings.

Findings

Improved variable selection in high-dimensional classification.

Effective reduction of false discovery rate during screening.

Successful application to simulated and real datasets.

Abstract

Variable selection in high-dimensional space characterizes many contemporary problems in scientific discovery and decision making. Many frequently-used techniques are based on independence screening; examples include correlation ranking (Fan and Lv, 2008) or feature selection using a two-sample t-test in high-dimensional classification (Tibshirani et al., 2003). Within the context of the linear model, Fan and Lv (2008)showed that this simple correlation ranking possesses a sure independence screening property under certain conditions and that its revision, called iteratively sure independent screening (ISIS), is needed when the features are marginally unrelated but jointly related to the response variable. In this paper, we extend ISIS, without explicit definition of residuals, to a general pseudo-likelihood framework, which includes generalized linear models as a special case. Even in the least-squares setting, the new method improves ISIS by allowing variable deletion in the iterative process. Our technique allows us to select important features in high-dimensional classification where the popularly used two-sample t-method fails. A new technique is introduced to reduce the false discovery rate in the feature screening stage. Several simulated and two real data examples are presented to illustrate the methodology.