GAP Safe screening rules for sparse multi-task and multi-class models
This work addresses efficiency improvements for high-dimensional regression in machine learning, though it is incremental as it builds on existing safe screening methods.
The paper tackles the problem of speeding up sparse regression solvers by developing new safe screening rules for generalized linear models with ℓ1 and ℓ1/ℓ2 norms, based on duality gap computations and spherical safe regions, resulting in significant speed-ups on tested datasets compared to previous safe rules.
High dimensional regression benefits from sparsity promoting regularizations. Screening rules leverage the known sparsity of the solution by ignoring some variables in the optimization, hence speeding up solvers. When the procedure is proven not to discard features wrongly the rules are said to be \emph{safe}. In this paper we derive new safe rules for generalized linear models regularized with $\ell_1$ and $\ell_1/\ell_2$ norms. The rules are based on duality gap computations and spherical safe regions whose diameters converge to zero. This allows to discard safely more variables, in particular for low regularization parameters. The GAP Safe rule can cope with any iterative solver and we illustrate its performance on coordinate descent for multi-task Lasso, binary and multinomial logistic regression, demonstrating significant speed ups on all tested datasets with respect to previous safe rules.