We give safe screening rules to eliminate variables from regression with L0 regularization or cardinality constraint. These rules are based on guarantees that a feature may or may not be selected in an optimal solution. The screening rules can be computed from a convex relaxation solution in linear time, without solving the L0 optimization problem. Thus, they can be used in a preprocessing step to safely remove variables from consideration apriori. Numerical experiments on real and synthetic data indicate that, on average, 76% of the variables can be fixed to their optimal values, hence, reducing the computational burden for optimization substantially. Therefore, the proposed fast and effective screening rules extend the scope of algorithms for L0-regression to larger data sets.
Research report, ISE, University of Southern California, February 2020