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.

翻译：我们研究一个通用的异质输出渠道的低位矩阵估计,通过这个渠道观察该矩阵。这概括了通常认为带有同一噪声的峰值矩阵模型,例如包括密集度校正的随机区块模型。我们调整了用于研究多物种旋转眼镜的技术,以得出并严格证明大尺寸限制的问题的自由能量的表达方式,为研究信号检测阈值提供了一个框架。我们讨论了将这一框架应用到经纠正的随机区块模型的程度。