论文标题
低排名PSD矩阵的排名一测量值
Rank-One Measurements of Low-Rank PSD Matrices Have Small Feasible Sets
论文作者
论文摘要
我们研究了设置在确定对低级别的阳性半芬酸盐（PSD）矩阵传感问题的解决方案方面的作用。我们考虑的设置涉及等级的传感矩阵：尤其是，给定一组级别的一组投影，大约是较低的PSD矩阵，我们表征了满足测量值的PSD矩阵的半径。当真矩阵完全低级别时，该结果产生了一个采样率，以确保单例解集合，从而选择目标函数或要使用的算法的选择在其恢复中无关紧要。我们讨论了此贡献的应用，并将其与有关类似问题的隐式正则化的最新文献进行了比较。我们通过应用圆锥投影方法进行PSD矩阵恢复而不纳入低级别的正则化，从而证明了该结果的实际含义。
We study the role of the constraint set in determining the solution to low-rank, positive semidefinite (PSD) matrix sensing problems. The setting we consider involves rank-one sensing matrices: In particular, given a set of rank-one projections of an approximately low-rank PSD matrix, we characterize the radius of the set of PSD matrices that satisfy the measurements. This result yields a sampling rate to guarantee singleton solution sets when the true matrix is exactly low-rank, such that the choice of the objective function or the algorithm to be used is inconsequential in its recovery. We discuss applications of this contribution and compare it to recent literature regarding implicit regularization for similar problems. We demonstrate practical implications of this result by applying conic projection methods for PSD matrix recovery without incorporating low-rank regularization.
