论文标题
拉索型最小化器的稀疏性
The Sparsity of LASSO-type Minimizers
论文作者
论文摘要
本说明将套索过程的属性扩展到了一类相关过程，包括方形拉索，方形拉索，lad-lasso和广义套索实例。 Namely, under the assumption that the input matrix satisfies an $\ell_p$-restricted isometry property (which in some sense is weaker than the standard $\ell_2$-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测得的向量。当正则化参数不小时，在存在中等测量误差的情况下，该结果仍然有效。
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 $\ell_p$-restricted isometry property (which in some sense is weaker than the standard $\ell_2$-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.
