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A common approach for compressing large-scale data is through matrixsketching. In this work, we consider the problem of recovering low-rankmatrices from two noisy linear sketches using the double sketching schemediscussed in Fazel et al. (2008), which is based on an approach by Woolfe etal. (2008). Using tools from non-asymptotic random matrix theory, we providethe first theoretical guarantees characterizing the error between the output ofthe double sketch algorithm and the ground truth low-rank matrix. We apply ourresult to the problems of low-rank matrix approximation and low-tubal-ranktensor recovery.

Robust recovery of low-rank matrices and low-tubal-rank tensors from noisy sketches