  We consider rules for discarding predictors in lasso regression and related
problems, for computational efficiency. El Ghaoui et al (2010) propose "SAFE"
rules that guarantee that a coefficient will be zero in the solution, based on
the inner products of each predictor with the outcome. In this paper we propose
strong rules that are not foolproof but rarely fail in practice. These can be
complemented with simple checks of the Karush- Kuhn-Tucker (KKT) conditions to
provide safe rules that offer substantial speed and space savings in a variety
of statistical convex optimization problems.
