High dimensional deformed rectangular matrices with applications in matrix denoising

Abstract

We consider the recovery of a low rank $M\times N$ matrix $S$ from its noisy observation $\tilde{S}$ in two different regimes. Under the assumption that $M$ is comparable to $N$, we propose two consistent estimators for $S$. Our analysis relies on the local behavior of the large dimensional rectangular matrices with finite rank perturbation. We also derive the convergent limits and rates for the singular values and vectors of such matrices.

References in corpus (2)

• Factor modeling for high-dimensional time series: Inference for the number of factors
• Rate Optimal Denoising of Simultaneously Sparse and Low Rank Matrices

Cited by in corpus (3)

• Adapting to Unknown Noise Distribution in Matrix Denoising
• Confidence Region of Singular Subspaces for Low-rank Matrix Regression
• Modified Multidimensional Scaling and High Dimensional Clustering