论文标题
通过协方差拟合调整了线性回归的正则化估计器
Tuned Regularized Estimators for Linear Regression via Covariance Fitting
论文作者
论文摘要
我们考虑为线性模型找到调整的正则参数估计器的问题。首先，我们表明三个已知的最佳线性估计器属于更广泛的估计器类别，这些估计量可以作为解决加权和约束最小化问题的解决方案。但是，在许多应用中，最佳权重通常是未知的。这就提出了一个问题，我们应该如何仅使用数据选择权重？我们建议使用协方差拟合Spice方法学获取数据自适应权重，并表明所得类别的估计器会产生已知的正则估计量的调整版本，例如Ridge Recression，Lasso和正规化的绝对绝对偏差。这些理论上的结果统一了普通保护伞下的几个重要估计量。通过许多数值示例，所得的调谐估计器实际上与实际相关。
We consider the problem of finding tuned regularized parameter estimators for linear models. We start by showing that three known optimal linear estimators belong to a wider class of estimators that can be formulated as a solution to a weighted and constrained minimization problem. The optimal weights, however, are typically unknown in many applications. This begs the question, how should we choose the weights using only the data? We propose using the covariance fitting SPICE-methodology to obtain data-adaptive weights and show that the resulting class of estimators yields tuned versions of known regularized estimators - such as ridge regression, LASSO, and regularized least absolute deviation. These theoretical results unify several important estimators under a common umbrella. The resulting tuned estimators are also shown to be practically relevant by means of a number of numerical examples.
