稀疏信号的圆锥松弛精确恢复
On the exact recovery of sparse signals via conic relaxations
摘要：
在这篇文章中，我们比较了Pilanci，Wainwright和El Ghaoui最近提出的稀疏线性回归问题的两个半定松弛（通过布尔松弛进行稀疏学习，2015）和Dong，Chen和Linderoth（松弛与正则化统计变量选择的圆锥优化观点，2015）。我们重点讨论了基数约束形式，证明了Dong等人提出的松弛理论并不弱于Pilanci等人提出的松弛，因此Pilanci等人导出的精确恢复的充分条件可以很容易地应用于其他松弛，包括他们关于高斯系综高概率恢复的结果.最后，我们提供的经验证据表明，放松董等。需要更少的观察，以保证恢复真正的支持。
英文摘要：
In this note we compare two recently proposed semidefinite relaxations for the sparse linear regression problem by Pilanci, Wainwright and El Ghaoui (Sparse learning via boolean relaxations, 2015) and Dong, Chen and Linderoth (Relaxation vs. Regularization A conic optimization perspective of statistical variable selection, 2015). We focus on the cardinality constrained formulation, and prove that the relaxation proposed by Dong, etc. is theoretically no weaker than the one proposed by Pilanci, etc. Therefore any sufficient condition of exact recovery derived by Pilanci can be readily applied to the other relaxation, including their results on high probability recovery for Gaussian ensemble. Finally we provide empirical evidence that the relaxation by Dong, etc. requires much fewer observations to guarantee the recovery of true support.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
