论文标题
低级矩阵估计与不均匀噪声
Low-rank Matrix Estimation with Inhomogeneous Noise
论文作者
论文摘要
我们研究了一个普通的不均匀输出通道的低级矩阵估计，观察到了基质。这概括了具有均匀噪声的普遍考虑的尖峰矩阵模型，例如密集程度校正的随机块模型。我们适应用于研究多种旋转玻璃的技术，以得出并严格地证明了在大尺寸限制下问题的自由能的表达，从而提供了一个研究信号检测阈值的框架。我们讨论了该框架在程度校正的随机块模型中的应用。
We study low-rank matrix estimation for a generic inhomogeneous output channel through which the matrix is observed. This generalizes the commonly considered spiked matrix model with homogeneous noise to include for instance the dense degree-corrected stochastic block model. We adapt techniques used to study multispecies spin glasses to derive and rigorously prove an expression for the free energy of the problem in the large size limit, providing a framework to study the signal detection thresholds. We discuss an application of this framework to the degree corrected stochastic block models.
