Differentially private and decentralized randomized power method

TMLR Paper6260 Authors

Abstract: 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 user 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 variance of the noise required in current techniques to achieve Differential Privacy (DP). More precisely, we modify the algorithm and privacy analysis so that the Gaussian noise variance no longer grows linearly with the target rank, achieving the same $(\varepsilon,\delta)$‑DP guarantees with lower noise variance. Second, we adapt our method to a decentralized framework in which data is distributed among multiple user devices, strengthening privacy guarantees with no accuracy penalty and a low computational and communication overhead. Our results also 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.

Submission Length: Regular submission (no more than 12 pages of main content)

Assigned Action Editor: ~Sinead_Williamson1

Submission Number: 6260