  Extracting relevant features from data sets where the number of observations
($n$) is much smaller then the number of predictors ($p$) is a major challenge
in modern statistics. Sorted L-One Penalized Estimation (SLOPE), a
generalization of the lasso, is a promising method within this setting. Current
numerical procedures for SLOPE, however, lack the efficiency that respective
tools for the lasso enjoy, particularly in the context of estimating a complete
regularization path. A key component in the efficiency of the lasso is
predictor screening rules: rules that allow predictors to be discarded before
estimating the model. This is the first paper to establish such a rule for
SLOPE. We develop a screening rule for SLOPE by examining its subdifferential
and show that this rule is a generalization of the strong rule for the lasso.
Our rule is heuristic, which means that it may discard predictors erroneously.
We present conditions under which this may happen and show that such situations
are rare and easily safeguarded against by a simple check of the optimality
conditions. Our numerical experiments show that the rule performs well in
practice, leading to improvements by orders of magnitude for data in the $p \gg
n$ domain, as well as incurring no additional computational overhead when $n
\gg p$. We also examine the effect of correlation structures in the design
matrix on the rule and discuss algorithmic strategies for employing the rule.
Finally, we provide an efficient implementation of the rule in our R package
SLOPE.
