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Analysis of singular subspaces under random perturbations

Ke Wang

Annals of Statistics2026https://doi.org/10.1214/25-aos2582article
AJG 4*ABDC A*
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0.50

What the paper says

We present a comprehensive analysis of singular vector and singular subspace perturbations in the signal-plus-noise matrix model with random Gaussian noise. Assuming a low-rank signal matrix, we extend the Davis–Kahan–Wedin theorem in a fully generalized manner, applicable to any unitarily invariant matrix norm, building on previous results by O’Rourke, Vu, and the author. Our analysis provides fine-grained insights, including ℓ∞ bounds for singular vectors, ℓ2,∞ bounds for singular subspaces, and results for linear and bilinear functions of singular vectors. Additionally, we derive ℓ2,∞ bounds on perturbed singular vectors, taking into account the weighting by their corresponding singular values. Finally, we explore practical implications of these results in the Gaussian mixture model and the submatrix localization problem.

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https://doi.org/https://doi.org/10.1214/25-aos2582

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@article{ke2026,
  title        = {{Analysis of singular subspaces under random perturbations}},
  author       = {Ke Wang},
  journal      = {Annals of Statistics},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.1214/25-aos2582},
}

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Analysis of singular subspaces under random perturbations

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Evidence weight

0.50

Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40

F · citation impact0.50 × 0.4 = 0.20
M · momentum0.50 × 0.15 = 0.07
V · venue signal0.50 × 0.05 = 0.03
R · text relevance †0.50 × 0.4 = 0.20

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