New SoS certificates certify nontrivial sparse singular values of random Gaussian and subgaussian matrices whenever n ≫ η²d^(2+ε), nearly matching low-degree and SQ lower bounds and yielding near-optimal robust estimation tradeoffs.
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SoS Certificates for Sparse Singular Values and Their Applications: Robust Statistics, Subspace Distortion, and More
New SoS certificates certify nontrivial sparse singular values of random Gaussian and subgaussian matrices whenever n ≫ η²d^(2+ε), nearly matching low-degree and SQ lower bounds and yielding near-optimal robust estimation tradeoffs.