Concave 1-norm group selection.
Concave 1-norm group selection.
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DOI：
10.1093/biostatistics/kxu050
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发表时间：
2015-04
期刊：
影响因子：
2.1
通讯作者：
Dingfeng Jiang;Jian Huang
中科院分区：
文献类型：
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作者：
Dingfeng Jiang;Jian Huang
在许多高维问题中自然会出现分组结构。这些信息的结合可以改善模型拟合和变量选择。现有的组选择方法，如组Lasso，需要正确的成员。然而，在实践中，很难正确地指定所有变量的组成员关系。因此，开发对群体错误规范具有鲁棒性的群体选择方法非常重要。此外，在许多应用程序中，选择组和单个变量也是可取的。我们提出了一类凹[公式：见文本]-规范群惩罚，它对分组结构具有鲁棒性，可以执行双水平选择。提出了一种坐标下降算法来计算所提出的群体选择方法的解。在一定的正则性条件下，证明了算法的理论收敛性。与其他方法的比较表明，该方法在隶属度不规范情况下是最稳健的。仿真研究和实际数据应用表明，[公式：见文本]-范数凹群选择方法可以更好地控制错误发现率。在CRAN上可以找到一个R包来实现所提出的方法。
Grouping structures arise naturally in many high-dimensional problems. Incorporation of such information can improve model fitting and variable selection. Existing group selection methods, such as the group Lasso, require correct membership. However, in practice it can be difficult to correctly specify group membership of all variables. Thus, it is important to develop group selection methods that are robust against group mis-specification. Also, it is desirable to select groups as well as individual variables in many applications. We propose a class of concave [Formula: see text]-norm group penalties that is robust to grouping structure and can perform bi-level selection. A coordinate descent algorithm is developed to calculate solutions of the proposed group selection method. Theoretical convergence of the algorithm is proved under certain regularity conditions. Comparison with other methods suggests the proposed method is the most robust approach under membership mis-specification. Simulation studies and real data application indicate that the [Formula: see text]-norm concave group selection approach achieves better control of false discovery rates. An R package grppenalty implementing the proposed method is available at CRAN.