Establishes statistical and computational optimality thresholds for common subspace estimation and inference under varying SNR regimes, including an impossibility result for adaptive confidence intervals below strong inference SNR.
Tensor SVD : Statistical and Computational Limits
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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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Statistically and Computationally Optimal Estimation and Inference of Common Subspaces
Establishes statistical and computational optimality thresholds for common subspace estimation and inference under varying SNR regimes, including an impossibility result for adaptive confidence intervals below strong inference SNR.
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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.