论文标题
簇套索和奥斯卡的有效路径算法
Efficient Path Algorithms for Clustered Lasso and OSCAR
论文作者
论文摘要
在高维回归中，特征聚类对结果的影响通常与选择特征选择一样重要。为此，用于回归（OSCAR）的聚类拉索和八角形收缩和聚类算法分别通过成对$ l_1 $ norm和pairwise $ l_ \ infty $ norm自动使特征组自动制造。本文提出了簇的套索和奥斯卡群的有效路径算法，以相对于其正则化参数构建解决方案路径。尽管详尽的成对正规化术语过多，但使用这些术语的对称性降低了计算成本。简单的等效条件检查每个特征组中的亚级别方程都是由某些图理论得出的。在数值实验中，所提出的算法比现有算法更有效。
In high dimensional regression, feature clustering by their effects on outcomes is often as important as feature selection. For that purpose, clustered Lasso and octagonal shrinkage and clustering algorithm for regression (OSCAR) are used to make feature groups automatically by pairwise $L_1$ norm and pairwise $L_\infty$ norm, respectively. This paper proposes efficient path algorithms for clustered Lasso and OSCAR to construct solution paths with respect to their regularization parameters. Despite too many terms in exhaustive pairwise regularization, their computational costs are reduced by using symmetry of those terms. Simple equivalent conditions to check subgradient equations in each feature group are derived by some graph theories. The proposed algorithms are shown to be more efficient than existing algorithms in numerical experiments.
