On the Sparsity of LASSO Minimizers in Sparse Data Recovery
On the Sparsity of LASSO Minimizers in Sparse Data Recovery
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DOI：
10.1007/s00365-022-09594-1
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发表时间：
2020-04
影响因子：
2.7
通讯作者：
S. Foucart;E. Tadmor;Ming Zhong
中科院分区：
文献类型：
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作者：
S. Foucart;E. Tadmor;Ming Zhong
我们详细分析了无约束加权 LASSO 方法，该方法通过随机生成的矩阵从其观察中恢复稀疏数据，满足恒定的受限等距属性 (RIP)，并且测量误差和压缩误差可以忽略不计。我们证明，如果数据是稀疏的，那么 LASSO 最小化器的支持大小将保持相当的稀疏性。例如，如果那么产量稍小。我们还推导了新的误差界限，突出了对 LASSO 参数的精确依赖性，然后误差被驱动到可忽略的测量/和压缩误差的范围以下。
We present a detailed analysis of the unconstrained-weighted LASSO method for recovery of sparse data from its observation by randomly generated matrices, satisfying the restricted isometry property (RIP) with constant, and subject to negligible measurement and compressibility errors. We prove that if the data arek-sparse, then the size of support of the LASSO minimizer,s, maintains a comparable sparsity,. For example, ifthenand a slightly smalleryields. We also derive newerror bounds which highlight precise dependence onkand on the LASSO parameter, before the error is driven below the scale of negligible measurement/ and compressiblity errors.