Low-rank Matrix Estimation with Inhomogeneous Noise

Abstract

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.

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References in corpus (5)

• Stochastic blockmodels and community structure in networks
• Free energy in multi-species mixed $p$-spin spherical models
• Phase transitions and optimal algorithms in high-dimensional Gaussian mixture clustering
• An inference problem in a mismatched setting: a spin-glass model with Mattis interaction
• Crisanti-Sommers formula and simultaneous symmetry breaking in multi-species spherical spin glasses