关于模型选择中Lasso的峰值现象
On the Peaking Phenomenon of the Lasso in Model Selection
摘要：
我简要地报告了一些意想不到的结果，我优化Lasso的模型参数时获得的。在具有变化的观测变量比n=p的模拟中，我通常在过渡点n/p = 1处观察到测试误差曲线中的强峰值。这种峰值现象在涉及样本协方差阵求逆的场景中得到了很好的证明，正如我在本说明中所说明的，它也是Lasso峰值的来源。关键问题是Lasso惩罚的参数化（例如在当前的R包lars中），我提出了一个标准化Lasso参数的解决方案。
英文摘要：
I briefly report on some unexpected results that I obtained when optimizing the model parameters of the Lasso. In simulations with varying observations-to-variables ratio n=p, I typically observe a strong peak in the test error curve at the transition point n/p = 1. This peaking phenomenon is well-documented in scenarios that involve the inversion of the sample covariance matrix, and as I illustrate in this note, it is also the source of the peak for the Lasso. The key problem is the parametrization of the Lasso penalty (as e.g. in the current R package lars) and I present a solution in terms of a normalized Lasso parameter.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
