Safe Screening Rules for $\ell_0$-Regression
This work addresses computational efficiency for ℓ0-regression, enabling its application to larger datasets, though it is incremental as it builds on existing screening rule concepts.
The paper tackles the problem of variable selection in regression with ℓ0 regularization by developing safe screening rules that eliminate variables before optimization, based on guarantees from a convex relaxation. Numerical experiments show that on average, 76% of variables can be fixed to their optimal values, reducing computational burden.
We give safe screening rules to eliminate variables from regression with $\ell_0$ 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 $\ell_0$ 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 $\ell_0$-regression to larger data sets.