Tradeoffs in improved screening of lasso problems

Recently, methods of screening the lasso problem have been developed that use the target vector x to quickly identify a subset of columns of the dictionary that will receive zero weight in the solution. Current classes of screening tests are based on bounding the dual lasso solution within a sphere or the intersection of a sphere and a half space. Stronger tests are possible but are more complex and incur a higher computational cost. To investigate this, we determine the optimal screening test when the dual lasso solution is bounded within the intersection of a sphere and two half spaces, and empirically investigate the trade-off that this test makes between screening power and computational efficiency. We also compare its performance both in terms of rejection power and efficiency to existing test classes. The new test always has better rejection, and for an interesting range of regularization parameters, offers better computational efficiency.