# Adaptive Power Iteration Method for Differentially Private PCA

arXiv: https://arxiv.org/abs/2602.11454 · HTML: https://mlsanity.com/paper/2602.11454/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 32 references that are in the map.
- First posted on arXiv 12 Feb 2026.

## Builds on (most cited first, 16 of 16)

- [The Noisy Power Method: A Meta Algorithm with Applications](https://mlsanity.com/paper/1311.2495/) (2013)
- [Covariance-Aware Private Mean Estimation Without Private Covariance Estimation](https://mlsanity.com/paper/2106.13329/) (2021)
- [Streaming PCA: Matching Matrix Bernstein and Near-Optimal Finite Sample Guarantees for Oja's Algorithm](https://mlsanity.com/paper/1602.06929/) (2016)
- [An Improved Gap-Dependency Analysis of the Noisy Power Method](https://mlsanity.com/paper/1602.07046/) (2016)
- [DP-PCA: Statistically Optimal and Differentially Private PCA](https://mlsanity.com/paper/2205.13709/) (2022)
- [Fast, Sample-Efficient, Affine-Invariant Private Mean and Covariance Estimation for Subgaussian Distributions](https://mlsanity.com/paper/2301.12250/) (2023)
- [Re-Analyze Gauss: Bounds for Private Matrix Approximation via Dyson Brownian Motion](https://mlsanity.com/paper/2211.06418/) (2022)
- [Insufficient Statistics Perturbation: Stable Estimators for Private Least Squares](https://mlsanity.com/paper/2404.15409/) (2024)
- [Differentially private and decentralized randomized power method](https://mlsanity.com/paper/2411.01931/) (2024)
- [Private Low-Rank Approximation for Covariance Matrices, Dyson Brownian Motion, and Eigenvalue-Gap Bounds for Gaussian Perturbations](https://mlsanity.com/paper/2502.07657/) (2025)
- [Better Private Linear Regression Through Better Private Feature Selection](https://mlsanity.com/paper/2306.00920/) (2023)
- [An Iterative Algorithm for Differentially Private k-PCA with Adaptive Noise](https://mlsanity.com/paper/2508.10879/) (2025)
- [Spectral Perturbation Bounds for Low-Rank Approximation with Applications to Privacy](https://mlsanity.com/paper/2510.25670/) (2025)
- [Tight Differentially Private PCA via Matrix Coherence](https://mlsanity.com/paper/2510.26679/) (2025)
- [Tukey Depth Mechanisms for Practical Private Mean Estimation](https://mlsanity.com/paper/2502.18698/) (2025)
- [Decentralized Differentially Private Power Method](https://mlsanity.com/paper/2507.22849/) (2025)

## Built on by (most cited first, 1 of 1)

- [Gap-free Differentially Private PCA for Gaussian Data](https://mlsanity.com/paper/2609.31614/) (2026)

## 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.