  l1-norm quantile regression is a common choice if there exists outlier or
heavy-tailed error in high-dimensional data sets. However, it is
computationally expensive to solve this problem when the feature size of data
is ultra high. As far as we know, existing screening rules can not speed up the
computation of the l1-norm quantile regression, which dues to the
non-differentiability of the quantile function/pinball loss. In this paper, we
introduce the dual circumscribed sphere technique and propose a novel l1-norm
quantile regression screening rule. Our rule is expressed as the closed-form
function of given data and eliminates inactive features with a low
computational cost. Numerical experiments on some simulation and real data sets
show that this screening rule can be used to eliminate almost all inactive
features. Moreover, this rule can help to reduce up to 23 times of
computational time, compared with the computation without our screening rule.
