The adaptive lasso refers to a class of methods that use weighted versions of the $L_1$-norm penalty, with weights derived from an initial estimate of the parameter vector to be estimated. Irrespective of the method chosen to compute this initial estimate, the performance of the adaptive lasso critically depends on the value of a hyperparameter, which controls the magnitude of the weighted $L_1$-norm in the penalized criterion. As for other machine learning methods, cross-validation is very popular for the calibration of the adaptive lasso, that this for the selection of a data-driven optimal value of this hyperparameter. However, the most simple cross-validation scheme is not valid in this context, and a more elaborate one has to be employed to guarantee an optimal calibration. The discrepancy of the simple cross-validation scheme has been well documented in other contexts, but less so when it comes to the calibration of the adaptive lasso, and, therefore, many statistical analysts still overlook it. In this work, we recall appropriate cross-validation schemes for the calibration of the adaptive lasso, and illustrate the discrepancy of the simple scheme, using both synthetic and real-world examples. Our results clearly establish the suboptimality of the simple scheme, in terms of support recovery and prediction error, for several versions of the adaptive lasso, including the popular one-step lasso.

翻译：调整 lasso 指的是使用 $_ 1 美元- 诺姆 罚款加权版本的一组方法,其加权值来自对参数矢量的初步估计。无论选择哪种方法来计算这一初步估计,适应 lasso 的性能关键取决于超参数值,后者控制了受处罚标准中加权值 $_ 1 美元- 诺姆的数值。与其他机器学习方法一样,交叉校准对于调整 lasso 校准非常受欢迎,用于选择数据驱动的这一超参数的最佳值。然而,最简单的交叉校准办法在此情况下并不有效,而更复杂的办法则用于保证最佳校准。简单交叉校准办法的差异在其他情况下都有详细记载,但在调整调适拉索的校准方面则较少,因此,许多统计分析师仍然如此忽略了它。在这项工作中,我们想起了用于校准这一数据驱动值最佳值的适当的交叉校准方案,包括简单综合办法的组合结果,并用简单的合成办法的模型说明我们若干次的恢复结果的差异。