  Lasso is a widely used regression technique to find sparse representations.
When the dimension of the feature space and the number of samples are extremely
large, solving the Lasso problem remains challenging. To improve the efficiency
of solving large-scale Lasso problems, El Ghaoui and his colleagues have
proposed the SAFE rules which are able to quickly identify the inactive
predictors, i.e., predictors that have $0$ components in the solution vector.
Then, the inactive predictors or features can be removed from the optimization
problem to reduce its scale. By transforming the standard Lasso to its dual
form, it can be shown that the inactive predictors include the set of inactive
constraints on the optimal dual solution. In this paper, we propose an
efficient and effective screening rule via Dual Polytope Projections (DPP),
which is mainly based on the uniqueness and nonexpansiveness of the optimal
dual solution due to the fact that the feasible set in the dual space is a
convex and closed polytope. Moreover, we show that our screening rule can be
extended to identify inactive groups in group Lasso. To the best of our
knowledge, there is currently no "exact" screening rule for group Lasso. We
have evaluated our screening rule using synthetic and real data sets. Results
show that our rule is more effective in identifying inactive predictors than
existing state-of-the-art screening rules for Lasso.
