mlsanityData to 7 Oct 2026

Adaptive Power Iteration Method for Differentially Private PCA

arXiv 2602.11454 ↗First posted 12 Feb 2026cs.DS cs.LGcited by 1

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Abstract (arXiv)

We study left(ε,δright)-differentially private algorithms for the problem of approximately computing the top singular vector of a matrix A∈ℝn× d where each row of A is a data point in ℝd. Following Dwork-Talwar-Thakurta-Zhang (STOC 2014), we consider the privacy model where neighboring inputs differ by one single row. We give a novel algorithm that achieves beyond-worst-case guarantees for input matrices with low coherence, which is a structural property of matrices in many applications, including but not limited to i.i.d. data. Our algorithm contributes to the extensive literature on private power iteration methods, where we introduce a new filtering technique which adapts to this coherence parameter. Our work departs from and complements the work by Hardt-Roth (STOC 2013) which achieves beyond-worst-case guarantees for the more restrictive privacy model where neighboring inputs differ in one single entry by at most 1.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 16 of its 32 references that are in the map. First posted on arXiv 12 Feb 2026.

Builds on

16 of 32 references.

References · 16

  1. 2013The Noisy Power Method: A Meta Algorithm with Applicationscited by 58
  2. 2021Covariance-Aware Private Mean Estimation Without Private Covariance Estimationcited by 46
  3. 2016Streaming PCA: Matching Matrix Bernstein and Near-Optimal Finite Sample Guarantees for Oja's Algorithmcited by 29
  4. 2016An Improved Gap-Dependency Analysis of the Noisy Power Methodcited by 24
  5. 2022DP-PCA: Statistically Optimal and Differentially Private PCAcited by 24
  6. 2023Fast, Sample-Efficient, Affine-Invariant Private Mean and Covariance Estimation for Subgaussian Distributionscited by 22
  7. 2022Re-Analyze Gauss: Bounds for Private Matrix Approximation via Dyson Brownian Motioncited by 8
  8. 2024Insufficient Statistics Perturbation: Stable Estimators for Private Least Squarescited by 7
  9. 2024Differentially private and decentralized randomized power methodcited by 6
  10. 2025Private Low-Rank Approximation for Covariance Matrices, Dyson Brownian Motion, and Eigenvalue-Gap Bounds for Gaussian Perturbationscited by 6
  11. 2023Better Private Linear Regression Through Better Private Feature Selectioncited by 5
  12. 2025An Iterative Algorithm for Differentially Private k-PCA with Adaptive Noisecited by 3
4 more
  1. 2025Spectral Perturbation Bounds for Low-Rank Approximation with Applications to Privacycited by 3
  2. 2025Tukey Depth Mechanisms for Practical Private Mean Estimationcited by 2
  3. 2025Tight Differentially Private PCA via Matrix Coherencecited by 2
  4. 2025Decentralized Differentially Private Power Methodcited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Gap-free Differentially Private PCA for Gaussian Datacited by 0