Laplace Error Penalty‐based Variable Selection in High Dimension
Laplace Error Penalty‐based Variable Selection in High Dimension
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DOI：
10.1111/sjos.12130
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发表时间：
2015-09
影响因子：
1
通讯作者：
Canhong Wen;Xueqin Wang;Shaoli Wang
中科院分区：
文献类型：
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作者：
Canhong Wen;Xueqin Wang;Shaoli Wang
我们提出了用于高维回归变量选择的拉普拉斯误差惩罚（LEP）函数。与使用分段样条构造的罚函数不同，LEP被构造为具有两个可调参数的指数函数，并且除原点外在任何地方都是无限可微的。通过这种结构，基于LEP的过程在变量选择上获得了额外的灵活性，在优化中允许统一的导数公式，并且能够尽可能接近L0惩罚。我们表明，LEP程序可以识别出具有正态误差的指数高维回归的相关预测因子。我们还建立了LEP估计器的oracle性质。虽然LEP不是凸的，但如果p不大于n，在温和的条件下，LEP产生凸惩罚最小二乘函数。引入了坐标下降最大化最小化算法来实现LEP过程。在模拟和实际数据分析中，LEP方法在竞争程序中表现良好。
We propose the Laplace Error Penalty (LEP) function for variable selection in high‐dimensional regression. Unlike penalty functions using piecewise splines construction, the LEP is constructed as an exponential function with two tuning parameters and is infinitely differentiable everywhere except at the origin. With this construction, the LEP‐based procedure acquires extra flexibility in variable selection, admits a unified derivative formula in optimization and is able to approximate the L0 penalty as close as possible. We show that the LEP procedure can identify relevant predictors in exponentially high‐dimensional regression with normal errors. We also establish the oracle property for the LEP estimator. Although not being convex, the LEP yields a convex penalized least squares function under mild conditions if p is no greater than n. A coordinate descent majorization‐minimization algorithm is introduced to implement the LEP procedure. In simulations and a real data analysis, the LEP methodology performs favorably among competitive procedures.