High-Dimensional Screening Using Multiple Grouping of Variables
This addresses screening in high-dimensional statistics for researchers and practitioners, offering a method that is incremental as it builds on existing group-based variable selection techniques.
The paper tackles the problem of screening to identify non-zero entries in a high-dimensional vector from noisy observations, proposing the Multiple Grouping (MuG) framework that groups variables and intersects results from repeated selections, and shows it enables consistent screening without tuning parameters when used with group Lasso, with numerical simulations demonstrating practical merits.
Screening is the problem of finding a superset of the set of non-zero entries in an unknown p-dimensional vector β* 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 β*. 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.