mlsanityData to 7 Oct 2026

Entrywise Recovery Guarantees for Sparse PCA via Sparsistent Algorithms

arXiv 2202.04061 ↗First posted 8 Feb 2022math.ST stat.ML stat.THcited by 0

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Abstract (arXiv)

Sparse Principal Component Analysis (PCA) is a prevalent tool across a plethora of subfields of applied statistics. While several results have characterized the recovery error of the principal eigenvectors, these are typically in spectral or Frobenius norms. In this paper, we provide entrywise ℓ2,∞ bounds for Sparse PCA under a general high-dimensional subgaussian design. In particular, our results hold for any algorithm that selects the correct support with high probability, those that are sparsistent. Our bound improves upon known results by providing a finer characterization of the estimation error, and our proof uses techniques recently developed for entrywise subspace perturbation theory.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 21 of its 71 references that are in the map. First posted on arXiv 8 Feb 2022.

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21 of 71 references.

References · 21

  1. 2020Spectral Methods for Data Science: A Statistical Perspectivecited by 111
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  12. 2021Entrywise Estimation of Singular Vectors of Low-Rank Matrices with Heteroskedasticity and Dependencecited by 12
9 more
  1. 2013Do semidefinite relaxations solve sparse PCA up to the information limit?cited by 9
  2. 2017Asymptotically efficient estimators for stochastic blockmodels: the naive MLE, the rank-constrained MLE, and the spectralcited by 9
  3. 2014Sparsistency and agnostic inference in sparse PCAcited by 8
  4. 2018The eigenvalues of stochastic blockmodel graphscited by 7
  5. 2018Sparse spectral estimation with missing and corrupted measurementscited by 5
  6. 2020An ℓp theory of PCA and spectral clusteringcited by 4
  7. 2015Sparse Nonlinear Regression: Parameter Estimation and Asymptotic Inferencecited by 2
  8. 2018Bayesian Estimation of Sparse Spiked Covariance Matrices in High Dimensionscited by 2
  9. 2020Entrywise convergence of iterative methods for eigenproblemscited by 1

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