改进随机幂法隐私保护，降噪且支持分布式计算
Differentially private and decentralized randomized power method
- 通过更精细的隐私分析，降低高斯噪声方差
- 目标秩增加时噪声不再线性增长，同等隐私下噪声更少
- 适用于分布式场景，隐私强、开销低，推荐系统可直接用
随机幂法因其简洁高效，被广泛用于大规模谱分析和推荐任务。然而，当处理包含个人行为（如网页交互、搜索历史）的数据集时，其隐私风险显著。本文提出两种增强型隐私保护变体：首先，通过优化隐私分析，使高斯噪声方差不再随目标秩线性增长，在相同差分隐私（DP）保障下所需噪声更少；其次，将方法扩展至去中心化框架，数据由多个用户持有，该协议在不牺牲精度的前提下强化了隐私保护，且计算与通信开销极低。本文还给出了集中式与去中心化版本的更紧收敛界，并在真实推荐数据集上与先前方法进行了实证对比。
原文摘要 · Abstract (English)
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.
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