High-Dimensional Screening Using Multiple Grouping of Variables

TL;DR

The paper introduces a novel Multiple Grouping (MuG) framework for high-dimensional variable screening that improves the identification of non-zero entries in large vectors by combining grouping, repeated selection, and intersection, especially effective with group Lasso.

Contribution

It proposes the MuG framework for variable screening that can be combined with any group-based method and achieves consistent screening without tuning parameters in high-dimensional settings.

Findings

MuG improves screening accuracy in simulations.

MuG with group Lasso performs consistently without tuning.

Numerical results demonstrate practical advantages of MuG.

Abstract

Screening is the problem of finding a superset of the set of non-zero entries in an unknown p-dimensional vector \beta* given n noisy observations. Naturally, we want this superset to be as small as possible. We propose a novel framework for screening, which we refer to as Multiple Grouping (MuG), that groups variables, performs variable selection over the groups, and repeats this process multiple number of times to estimate a sequence of sets that contains the non-zero entries in \beta*. Screening is done by taking an intersection of all these estimated sets. The MuG framework can be used in conjunction with any group based variable selection algorithm. In the high-dimensional setting, where p >> n, we show that when MuG is used with the group Lasso estimator, screening can be consistently performed without using any tuning parameter. Our numerical simulations clearly show the merits of using the MuG framework in practice.