论文标题
拉索重新加载：一种具有压缩感应应用的变分分析观点
LASSO reloaded: a variational analysis perspective with applications to compressed sensing
论文作者
论文摘要
本文提供了对套索问题的不受约束公式的变异分析，在统计学习，信号处理和反问题中无处不在。特别是，我们为最佳值以及最佳解决方案的Lipschitz特性建立了平滑度结果，作为右侧（或测量向量）和正则化参数的功能。此外，我们展示了如何应用所提出的变分分析来研究最佳解决方案对调谐参数的敏感性，并通过subgaussian测量值进行压缩感测。我们的理论发现通过数值实验验证。
This paper provides a variational analysis of the unconstrained formulation of the LASSO problem, ubiquitous in statistical learning, signal processing, and inverse problems. In particular, we establish smoothness results for the optimal value as well as Lipschitz properties of the optimal solution as functions of the right-hand side (or measurement vector) and the regularization parameter. Moreover, we show how to apply the proposed variational analysis to study the sensitivity of the optimal solution to the tuning parameter in the context of compressed sensing with subgaussian measurements. Our theoretical findings are validated by numerical experiments.
