SVD provably recovers the uncorrupted nearest neighbor from noisy data when σ is O(1/k^{1/4}), with a matching lower bound showing the threshold is necessary.
Random perturbation of low rank matrices: Improving classical bounds
2 Pith papers cite this work. Polarity classification is still indexing.
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Proves approximate Gaussianity of debiased linear forms of eigenvectors in matrix denoising and spiked PCA models under Gaussian noise, then constructs bias/variance estimators yielding minimax-optimal confidence intervals without sample splitting.
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SVD Provably Denoises Nearest Neighbor Data
SVD provably recovers the uncorrupted nearest neighbor from noisy data when σ is O(1/k^{1/4}), with a matching lower bound showing the threshold is necessary.
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Statistical Inference for Linear Functions of Eigenvectors with Small Eigengaps
Proves approximate Gaussianity of debiased linear forms of eigenvectors in matrix denoising and spiked PCA models under Gaussian noise, then constructs bias/variance estimators yielding minimax-optimal confidence intervals without sample splitting.