论文标题
当设计矩阵正交时，模式恢复和信号通过斜率降低了
Pattern recovery and signal denoising by SLOPE when the design matrix is orthogonal
论文作者
论文摘要
排序的$ \ ell_1 $惩罚估算器（斜率）是一种相对较新的凸正则化方法，用于拟合高维回归模型。坡度可以通过将回归系数的一些估计值缩小到零或等于这些系数的某些非零估计的绝对值来减少模型维度。这允许确定某些〜真正回归系数相等的情况。在本文中，我们将介绍斜率模式，即真实回归系数之间的一系列关系，可以通过斜率识别。当设计矩阵正交时，我们还将为斜率估计器的强一致性以及图案恢复的强段一致性提供新的结果，并说明在高频信号降解的背景下〜斜率群集的优势。
Sorted $\ell_1$ Penalized Estimator (SLOPE) is a relatively new convex regularization method for fitting high-dimensional regression models. SLOPE allows to reduce the model dimension by shrinking some estimates of the regression coefficients completely to zero or by equating the absolute values of some nonzero estimates of these coefficients. This allows to identify situations where some of~true regression coefficients are equal. In this article we will introduce the SLOPE pattern, i.e., the set of relations between the true regression coefficients, which can be identified by SLOPE. We will also present new results on the strong consistency of SLOPE estimators and on~the~strong consistency of pattern recovery by~SLOPE when the design matrix is orthogonal and illustrate advantages of~the~SLOPE clustering in the context of high frequency signal denoising.
