mlsanityData to 14 Oct 2026

Gap-free Differentially Private PCA for Gaussian Data

arXiv 2609.31614 ↗First posted 25 Sep 2026cs.DS cs.LGcited by 0

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Abstract (arXiv)

We give a gap-free (ε,δ)-differentially private algorithm for the principal component analysis (PCA) problem with Gaussian data. The algorithm is based on a private variant of the power iteration method, and it is computationally efficient.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 11 of its 16 references that are in the map. First posted on arXiv 25 Sep 2026.

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11 of 16 references.

References · 11

  1. 2017Finite Sample Differentially Private Confidence Intervalscited by 104
  2. 2021Differential privacy and robust statistics in high dimensionscited by 64
  3. 2013The Noisy Power Method: A Meta Algorithm with Applicationscited by 58
  4. 2023High Probability Convergence of Stochastic Gradient Methodscited by 49
  5. 2016First Efficient Convergence for Streaming k-PCA: a Global, Gap-Free, and Near-Optimal Ratecited by 32
  6. 2016An Improved Gap-Dependency Analysis of the Noisy Power Methodcited by 24
  7. 2022DP-PCA: Statistically Optimal and Differentially Private PCAcited by 24
  8. 2015Convergence of Stochastic Gradient Descent for PCAcited by 17
  9. 2025Tight Differentially Private PCA via Matrix Coherencecited by 3
  10. 2026Adaptive Power Iteration Method for Differentially Private PCAcited by 1
  11. 2026Gap-Free Streaming PCA Beyond Rank-One Updates: Near-Optimal Rates and Applications to Differential Privacycited by 1

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