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arXiv · 2602.11454

Adaptive Power Iteration Method for Differentially Private PCA

Ta Duy Nguyen·Alina Ene·Huy Le Nguyen
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Abstract

We study $\left(\epsilon,\delta\right)$-differentially private algorithms for the problem of approximately computing the top singular vector of a matrix $A\in\mathbb{R}^{n\times d}$ where each row of $A$ is a data point in $\mathbb{R}^{d}$. 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.

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Ta Duy Nguyen, Alina Ene, Huy Le Nguyen. 2026-02-12. Adaptive Power Iteration Method for Differentially Private PCA. https://arxiv.org/abs/2602.11454

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