  Sparse learning techniques have been routinely used for feature selection as
the resulting model usually has a small number of non-zero entries. Safe
screening, which eliminates the features that are guaranteed to have zero
coefficients for a certain value of the regularization parameter, is a
technique for improving the computational efficiency. Safe screening is gaining
increasing attention since 1) solving sparse learning formulations usually has
a high computational cost especially when the number of features is large and
2) one needs to try several regularization parameters to select a suitable
model. In this paper, we propose an approach called "Sasvi" (Safe screening
with variational inequalities). Sasvi makes use of the variational inequality
that provides the sufficient and necessary optimality condition for the dual
problem. Several existing approaches for Lasso screening can be casted as
relaxed versions of the proposed Sasvi, thus Sasvi provides a stronger safe
screening rule. We further study the monotone properties of Sasvi for Lasso,
based on which a sure removal regularization parameter can be identified for
each feature. Experimental results on both synthetic and real data sets are
reported to demonstrate the effectiveness of the proposed Sasvi for Lasso
screening.
