Fast lasso screening tests based on correlations

Representing a vector as a sparse linear combination of codewords, e.g. by solving a lasso problem, lies at the heart of many machine learning and statistics applications. To improve the efficiency of solving lasso problems, we systematically investigate lasso screening, a process that quickly identifies dictionary entries that won't be used in the optimal sparse representation, and hence can be removed from the problem. We propose a general test called an R region test that unifies existing screening tests and we derive a particular instance called the dome test. This test is stronger than existing screening tests and can be executed in linear-time as a two-pass test with a memory footprint of only three codewords.