In high dimensional regression context, sparsity enforcing penalties have proved useful to regularize the data-fitting term. A recently introduced technique called \emph{screening rules}, leverage the expected sparsity of the solutions by ignoring some variables in the optimization, hence leading to solver speed-ups. When the procedure is guaranteed not to discard features wrongly the rules are said to be \emph{safe}. We propose a unifying framework that can cope with generalized linear models regularized with standard sparsity enforcing penalties such as $\ell_1$ or $\ell_1/\ell_2$ norms. Our technique allows to discard safely more variables than previously considered safe rules, particularly for low regularization parameters. Our proposed Gap Safe rules (so called because they rely on duality gap computation) can cope with any iterative solver but is particularly well suited to block coordinate descent for many standard learning tasks: Lasso, Sparse-Group Lasso, multi-task Lasso, binary and multinomial logistic regression, etc. For all such tasks and on all tested datasets, we report significant speed-ups compared to previously proposed safe rules.

本研究提出了一种适用于广义线性模型的一体化框架，用标准的稀疏性惩罚（如l1或l1 / l2范数）进行正则化。我们的技术允许安全地丢弃比以前认为的安全规则更多的变量，特别是对于低正则化参数。应用于许多标准学习任务，如Lasso、Sparse-Group Lasso、多任务Lasso、二进制和多项式逻辑回归等，我们报告了比以前提出的所有测试数据集上的安全规则所获得的显著加速的更好的Gap Safe规则。

稀疏约束罚函数的间隔安全筛选规则