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[2602.11454] Adaptive Power Iteration Method for Differentially Private PCA
Summary
This paper presents an adaptive power iteration method for computing the top singular vector of a matrix while ensuring differential privacy, improving utility for matrices with low coherence.
Why It Matters
Differential privacy is crucial for protecting individual data in machine learning applications. This research enhances existing methods by providing better utility guarantees, which can lead to more effective and privacy-preserving data analysis techniques in various fields.
Key Takeaways
- Introduces an adaptive power iteration method for PCA under differential privacy.
- Improves utility for matrices with low coherence compared to previous methods.
- Addresses privacy concerns by ensuring neighboring inputs differ by one row.
- Builds on and complements earlier work in private power iteration methods.
- Provides a framework for future research in differentially private algorithms.
Computer Science > Data Structures and Algorithms arXiv:2602.11454 (cs) [Submitted on 12 Feb 2026 (v1), last revised 13 Feb 2026 (this version, v2)] Title:Adaptive Power Iteration Method for Differentially Private PCA Authors:Ta Duy Nguyen, Alina Ene, Huy Le Nguyen View a PDF of the paper titled Adaptive Power Iteration Method for Differentially Private PCA, by Ta Duy Nguyen and 2 other authors View PDF HTML (experimental) Abstract:We study $(\epsilon,\delta)$-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 datapoint in $\mathbb{R}^{d}$. In our privacy model, neighboring inputs differ by one single row/datapoint. We study the private variant of the power iteration method, which is widely adopted in practice. Our algorithm is based on a filtering technique which adapts to the coherence parameter of the input matrix. This technique provides a utility that goes beyond the worst-case guarantees for matrices with low coherence parameter. Our work departs from and complements the work by Hardt-Roth (STOC 2013) which designed a private power iteration method for the privacy model where neighboring inputs differ in one single entry by at most 1. Subjects: Data Structures and Algorithms (cs.DS); Machine Learning (cs.LG) Cite as: arXiv:2602.11454 [cs.DS] (or arXiv:2602.11454v2 [cs.DS] for this version) https://doi.org/10.48550/arXiv.2602.11454 Focus to learn m...
