COORDINATE DESCENT ALGORITHMS FOR NONCONVEX PENALIZED REGRESSION, WITH APPLICATIONS TO BIOLOGICAL FEATURE SELECTION.
COORDINATE DESCENT ALGORITHMS FOR NONCONVEX PENALIZED REGRESSION, WITH APPLICATIONS TO BIOLOGICAL FEATURE SELECTION.
复制标题
DOI：
10.1214/10-aoas388
复制
发表时间：
2011-01-01
期刊：
影响因子：
--
通讯作者：
Huang J
中科院分区：
文献类型：
--
作者：
Breheny P;Huang J
许多涉及非凸惩罚函数的变量选择方法已经被提出。这些方法，包括平滑剪裁绝对偏差（SCAD）惩罚和极大极小凹惩罚（MCP），已被证明具有吸引人的理论性质，但模型拟合不是一项简单的任务，所得解可能不稳定。在这里，我们展示了坐标下降算法拟合这些模型的潜力，建立了理论收敛性质，并证明它们比竞争方法要快得多。此外，我们证明了凸性诊断的效用，以确定参数空间的区域，其中目标函数是局部凸的，即使惩罚不是。我们的仿真研究和数据实例表明，在许多应用中，像MCP和SCAD这样的非凸惩罚是值得替代套索的。特别是，我们的数值结果表明，在三种方法中，MCP是首选的方法。
A number of variable selection methods have been proposed involving nonconvex penalty functions. These methods, which include the smoothly clipped absolute deviation (SCAD) penalty and the minimax concave penalty (MCP), have been demonstrated to have attractive theoretical properties, but model fitting is not a straightforward task, and the resulting solutions may be unstable. Here, we demonstrate the potential of coordinate descent algorithms for fitting these models, establishing theoretical convergence properties and demonstrating that they are significantly faster than competing approaches. In addition, we demonstrate the utility of convexity diagnostics to determine regions of the parameter space in which the objective function is locally convex, even though the penalty is not. Our simulation study and data examples indicate that nonconvex penalties like MCP and SCAD are worthwhile alternatives to the lasso in many applications. In particular, our numerical results suggest that MCP is the preferred approach among the three methods.