The model selected by sparse learning techniques usually has a few non-zero entries. Safe screening---which eliminates the features that are guaranteed to be absent for a target regularization parameter based on an existing solution---is a technique for improving the computational efficiency while maintaining the same solution. In this note, we propose an approach called Sasvi (Safe screening with variational inequalities) and take LASSO for example in the analysis. Sasvi makes use of the variational inequalities which provide the sufficient and necessary optimality conditions for the dual problem. The existing approaches can be casted as relaxed versions of the proposed Sasvi, and thus Sasvi provides a much stronger screening rule. The monotone properties of Sasvi are studied based on which a sure removal regularization parameter can be identified for each feature. In addition, the proposed Sasvi is readily extended for solving the generalized sparse linear models. Preliminary experimental results are reported.

本文介绍了一种名为“Sasvi”的方法，它基于变分不等式提供了更强的安全筛选规则，可用于稀疏学习模型的特征选择和计算效率优化。实验结果表明，Sasvi对Lasso筛选具有很强的可靠性和有效性。

用变分不等式实现安全筛选及其在 LASSO 中的应用