论文标题
斜坡的模式恢复
Pattern recovery by SLOPE
论文作者
论文摘要
坡度是降低高维回归中维数的流行方法。实际上，斜率的某些回归系数估计值可能为null（稀疏性），也可以在绝对值（聚类）中相等。因此，斜率可能会消除无关的预测因子，并可以识别对响应向量具有相同影响的预测变量组。斜率模式的概念允许在稀疏性和斜率聚类上得出理论特性。具体而言，向量的斜率模式提供了：其组件的符号（正，负或零）的符号，簇（组件的索引在绝对值中等于）和簇排名。在本文中，我们给出了一个必要且充分的条件，以恢复未知的回归系数向量。
SLOPE is a popular method for dimensionality reduction in the high-dimensional regression. Indeed some regression coefficient estimates of SLOPE can be null (sparsity) or can be equal in absolute value (clustering). Consequently, SLOPE may eliminate irrelevant predictors and may identify groups of predictors having the same influence on the vector of responses. The notion of SLOPE pattern allows to derive theoretical properties on sparsity and clustering by SLOPE. Specifically, the SLOPE pattern of a vector provides: the sign of its components (positive, negative or null), the clusters (indices of components equal in absolute value) and clusters ranking. In this article we give a necessary and sufficient condition for SLOPE pattern recovery of an unknown vector of regression coefficients.
