  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.
