STANDARDIZATION AND THE GROUP LASSO PENALTY.
STANDARDIZATION AND THE GROUP LASSO PENALTY.
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DOI：
10.5705/ss.2011.075
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发表时间：
2012-07
影响因子：
1.4
通讯作者：
Tibshirani R
中科院分区：
文献类型：
--
作者：
Simon N;Tibshirani R
我们重新检查原组Lasso论文。该论文中的惩罚形式似乎是为具有不相关特征的问题而设计的，但统计界已将其用于具有相关特征的一般问题。我们证明了对于这种一般情况，具有不同惩罚矩阵选择的群套索通常更有效。我们对这个公式进行了深入的研究，并证明它与群包含的一致最强大的不变量检验密切相关。我们在真实和模拟的数据集上证明了这种方法——“标准化组套索”——比通常的组套索更有效。我们还将此扩展到脊组套索，以根据需要提供组内正则化。我们讨论了一种基于群智能坐标下降的简单算法来拟合这种标准化群套索和脊状群套索。
We re-examine the original Group Lasso paper of. The form of penalty in that paper seems to be designed for problems with uncorrelated features, but the statistical community has adopted it for general problems with correlated features. We show that for this general situation, a Group Lasso with a different choice of penalty matrix is generally more effective. We give insight into this formulation and show that it is intimately related to the uniformly most powerful invariant test for inclusion of a group. We demonstrate the efficacy of this method– the “standardized Group Lasso”– over the usual group lasso on real and simulated data sets. We also extend this to the Ridged Group Lasso to provide within group regularization as needed. We discuss a simple algorithm based on group-wise coordinate descent to fit both this standardized Group Lasso and Ridged Group Lasso.