Solving Generalized LASSO (GL) problems is challenging, particularly when analyzing many features with a complex interacting structure. Recent developments have found effective ways to identify inactive features so that they can be removed or aggregated to reduce the problem size before applying optimization solvers for learning. However, existing methods are mostly devoted to special cases of GL problems with special structures for feature interactions, such as chains or trees. Developing screening rules, particularly, safe screening rules to remove or aggregate features with general interaction structures, calls for a very different screening approach for GL problems. To tackle this challenge, we formulate the GL screening problem as a bound estimation problem in a large linear inequality system when solving them in the dual space. We propose a novel bound propagation algorithm for efficient safe screening for general GL problems, which can be further enhanced by developing novel transformation methods that can effectively decouple interactions among features. The proposed propagation and transformation methods are applicable with dynamic screening that can easily initiate the screening process while existing screening methods require the knowledge of the solution under a desirable regularization parameter. Experiments on both synthetic and real-world data demonstrate the effectiveness of the proposed screening method.

中文翻译：

---

广义LASSO的安全特征筛选


解决广义 LASSO (GL) 问题具有挑战性，特别是在分析具有复杂交互结构的许多特征时。最近的发展已经找到了识别不活动特征的有效方法，以便在应用优化求解器进行学习之前将其删除或聚合以减小问题大小。然而，现有的方法大多致力于解决具有特征交互的特殊结构（例如链或树）的 GL 问题的特殊情况。开发筛选规则，特别是安全筛选规则，以删除或聚合具有一般交互结构的特征，需要针对总账问题采用截然不同的筛选方法。为了应对这一挑战，我们在对偶空间中求解时，将 GL 筛选问题表述为大型线性不等式系统中的有界估计问题。我们提出了一种新颖的边界传播算法，用于对一般 GL 问题进行有效安全的筛选，可以通过开发能够有效解耦特征之间相互作用的新颖变换方法来进一步增强该算法。所提出的传播和变换方法适用于动态筛选，可以轻松地启动筛选过程，而现有筛选方法需要了解所需正则化参数下的解。对合成数据和真实数据的实验证明了所提出的筛选方法的有效性。