# Differentially private and decentralized randomized power method

arXiv: https://arxiv.org/abs/2411.01931 · HTML: https://mlsanity.com/paper/2411.01931/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 45 references that are in the map.
- First posted on arXiv 4 Nov 2024.

## Builds on (most cited first, 17 of 17)

- [LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2002.02126/) (2020)
- [Inverting Gradients -- How easy is it to break privacy in federated learning?](https://mlsanity.com/paper/2003.14053/) (2020)
- [Neural Graph Collaborative Filtering](https://mlsanity.com/paper/1905.08108/) (2019)
- [Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds](https://mlsanity.com/paper/1605.02065/) (2016)
- [Sketching as a Tool for Numerical Linear Algebra](https://mlsanity.com/paper/1411.4357/) (2014)
- [The Distributed Discrete Gaussian Mechanism for Federated Learning with Secure Aggregation](https://mlsanity.com/paper/2102.06387/) (2021)
- [FastSecAgg: Scalable Secure Aggregation for Privacy-Preserving Federated Learning](https://mlsanity.com/paper/2009.11248/) (2020)
- [The Noisy Power Method: A Meta Algorithm with Applications](https://mlsanity.com/paper/1311.2495/) (2013)
- [How Powerful is Graph Convolution for Recommendation?](https://mlsanity.com/paper/2108.07567/) (2021)
- [Blurring-Sharpening Process Models for Collaborative Filtering](https://mlsanity.com/paper/2211.09324/) (2022)
- [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)
- [Memory Limited, Streaming PCA](https://mlsanity.com/paper/1307.0032/) (2013)
- [Scalable and Differentially Private Distributed Aggregation in the Shuffled Model](https://mlsanity.com/paper/1906.08320/) (2019)
- [An Accurate, Scalable and Verifiable Protocol for Federated Differentially Private Averaging](https://mlsanity.com/paper/2006.07218/) (2020)
- [The Privacy Power of Correlated Noise in Decentralized Learning](https://mlsanity.com/paper/2405.01031/) (2024)
- [FedPower: Privacy-Preserving Distributed Eigenspace Estimation](https://mlsanity.com/paper/2103.00704/) (2021)

## Built on by (most cited first, 6 of 6)

- [An Iterative Algorithm for Differentially Private k-PCA with Adaptive Noise](https://mlsanity.com/paper/2508.10879/) (2025)
- [Differential Privacy Analysis of Decentralized Gossip Averaging under Varying Threat Models](https://mlsanity.com/paper/2505.19969/) (2025)
- [Exposing the Vulnerability of Decentralized Learning to Membership Inference Attacks Through the Lens of Graph Mixing](https://mlsanity.com/paper/2412.12837/) (2024)
- [Decentralized Differentially Private Power Method](https://mlsanity.com/paper/2507.22849/) (2025)
- [Adaptive Power Iteration Method for Differentially Private PCA](https://mlsanity.com/paper/2602.11454/) (2026)
- [Dropout-Robust Mechanisms for Differentially Private and Fully Decentralized Mean Estimation](https://mlsanity.com/paper/2506.03746/) (2025)

## Abstract (arXiv)

The randomized power method has gained significant interest due to its simplicity and efficient handling of large-scale spectral analysis and recommendation tasks. However, its application to large datasets containing personal information (e.g., web interactions, search history, personal tastes) raises critical privacy problems. This paper addresses these issues by proposing enhanced privacy-preserving variants of the method. First, we propose a variant that reduces the amount of the noise required in current techniques to achieve Differential Privacy (DP). More precisely, we refine the privacy analysis so that the Gaussian noise variance no longer grows linearly with the target rank, achieving the same DP guarantees with strictly less noise. Second, we adapt our method to a decentralized framework in which data is distributed among multiple users. The decentralized protocol strengthens privacy guarantees with no accuracy penalty and a low computational and communication overhead. Our results include the provision of tighter convergence bounds for both the centralized and decentralized versions, and an empirical comparison with previous work using real recommendation datasets.