The sparsity of LASSO-type minimizers
The sparsity of LASSO-type minimizers
复制标题
LASSO 型最小化器的稀疏性
DOI：
10.1016/j.acha.2022.10.004
复制
发表时间：
2023
影响因子：
2.5
通讯作者：
Foucart, Simon
中科院分区：
文献类型：
--
作者：
Foucart, Simon
本注释将 LASSO 过程的属性扩展到一整类相关过程，包括平方根 LASSO、平方 LASSO、LAD-LASSO 和广义 LASSO 的实例。即，假设输入矩阵满足 ℓ p 限制等距属性（在某种意义上比标准 ℓ 2 限制等距属性假设更弱），结果表明，如果输入向量来自稀疏向量的精确测量，则任何此类 LASSO 类型过程的最小化器都具有与测量向量的稀疏性相当的稀疏性。当正则化参数不太小时，在存在中等测量误差的情况下，结果仍然有效。
This note extends an attribute of the LASSO procedure to a whole class of related procedures, including square-root LASSO, square LASSO, LAD-LASSO, and an instance of generalized LASSO. Namely, under the assumption that the input matrix satisfies an ℓ p-restricted isometry property (which in some sense is weaker than the standard ℓ 2-restricted isometry property assumption), it is shown that if the input vector comes from the exact measurement of a sparse vector, then the minimizer of any such LASSO-type procedure has sparsity comparable to the sparsity of the measured vector. The result remains valid in the presence of moderate measurement error when the regularization parameter is not too small.