论文标题
极值的稀疏回归
Sparse Regression for Extreme Values
论文作者
论文摘要
我们研究选择与高维线性回归中极值相关的特征的问题。通常，在线性建模问题中，异常的极值或异常值的存在被认为是一种异常现象，应从数据中删除，或使用可靠的回归方法进行修复。但是，在许多情况下，回归建模的极端价值不是异常值，而是感兴趣的信号。例如，考虑来自尖峰神经元的痕迹，金融中的波动性或气候科学中的极端事件。在本文中，我们提出了一种用于极值稀疏高维线性回归的新方法，该方法是由子植物或广义正态分布激励的，我们称之为极值线性回归模型。对于我们的方法，我们利用$ \ ell_p $ norm损失，其中$ p $是一个大于两个的整数；我们证明，这种损失会增加极端值的重量。我们证明了具有LASSO惩罚的极值线性回归的一致性和可变选择的一致性，我们将其称为“极端套索”，我们还使用影响函数的概念分析了极值观测值对模型参数估计的理论影响。通过仿真研究和现实世界数据示例，我们表明，极端拉索的表现优于文献中目前用于选择与高维回归中极值相关的特征的其他方法。
We study the problem of selecting features associated with extreme values in high dimensional linear regression. Normally, in linear modeling problems, the presence of abnormal extreme values or outliers is considered an anomaly which should either be removed from the data or remedied using robust regression methods. In many situations, however, the extreme values in regression modeling are not outliers but rather the signals of interest; consider traces from spiking neurons, volatility in finance, or extreme events in climate science, for example. In this paper, we propose a new method for sparse high-dimensional linear regression for extreme values which is motivated by the Subbotin, or generalized normal distribution, which we call the extreme value linear regression model. For our method, we utilize an $\ell_p$ norm loss where $p$ is an even integer greater than two; we demonstrate that this loss increases the weight on extreme values. We prove consistency and variable selection consistency for the extreme value linear regression with a Lasso penalty, which we term the Extreme Lasso, and we also analyze the theoretical impact of extreme value observations on the model parameter estimates using the concept of influence functions. Through simulation studies and a real-world data example, we show that the Extreme Lasso outperforms other methods currently used in the literature for selecting features of interest associated with extreme values in high-dimensional regression.
