论文标题
用于坡度和准球面奥斯卡的精确溶液路径算法
An Exact Solution Path Algorithm for SLOPE and Quasi-Spherical OSCAR
论文作者
论文摘要
排序的$ L_1 $惩罚估计器（斜率）是一种适用于高维回归中绝对系数的正规化技术。通过在单调性约束下任意设置其正则重量$λ$，斜率可以具有各种特征选择和聚类属性。在重量调整时，所选功能及其簇非常敏感。此外，使用网格搜索方法，很难对其更改进行详尽的跟踪。这项研究提出了一种溶液路径算法，该算法为微调正规化权重中的斜率提供了完整而精确的解决方案。得出了一个简单的最佳条件，并用于指定解决方案路径的下一个分裂点。这项研究还提出了针对特征聚类的正则化序列$λ$的新设计，该设计称为回归（QS-Iscar）的准球形和八角形收缩和聚类算法。 QS-ISCAR的设计具有与球体最相似的正则化项的轮廓表面。在几种正则化序列设计中，通过模拟研究比较稀疏性和聚类性能。数值观察表明，QS-Iscar比其他设计更有效地执行特征聚类。
Sorted $L_1$ penalization estimator (SLOPE) is a regularization technique for sorted absolute coefficients in high-dimensional regression. By arbitrarily setting its regularization weights $λ$ under the monotonicity constraint, SLOPE can have various feature selection and clustering properties. On weight tuning, the selected features and their clusters are very sensitive to the tuning parameters. Moreover, the exhaustive tracking of their changes is difficult using grid search methods. This study presents a solution path algorithm that provides the complete and exact path of solutions for SLOPE in fine-tuning regularization weights. A simple optimality condition for SLOPE is derived and used to specify the next splitting point of the solution path. This study also proposes a new design of a regularization sequence $λ$ for feature clustering, which is called the quasi-spherical and octagonal shrinkage and clustering algorithm for regression (QS-OSCAR). QS-OSCAR is designed with a contour surface of the regularization terms most similar to a sphere. Among several regularization sequence designs, sparsity and clustering performance are compared through simulation studies. The numerical observations show that QS-OSCAR performs feature clustering more efficiently than other designs.
