  We describe a fast method to eliminate features (variables) in l1 -penalized
least-square regression (or LASSO) problems. The elimination of features leads
to a potentially substantial reduction in running time, specially for large
values of the penalty parameter. Our method is not heuristic: it only
eliminates features that are guaranteed to be absent after solving the LASSO
problem. The feature elimination step is easy to parallelize and can test each
feature for elimination independently. Moreover, the computational effort of
our method is negligible compared to that of solving the LASSO problem -
roughly it is the same as single gradient step. Our method extends the scope of
existing LASSO algorithms to treat larger data sets, previously out of their
reach. We show how our method can be extended to general l1 -penalized convex
problems and present preliminary results for the Sparse Support Vector Machine
and Logistic Regression problems.
