用高斯投影提升隐私保护，让线性回归更安全高效
The Gaussian Mixing Mechanism: Renyi Differential Privacy via Gaussian Sketches
- 用随机高斯矩阵对数据预处理，天然带来隐私保护
- 新分析方法使隐私预算降低30%以上，理论更严格
- 在多个数据集上提速且保持高精度，适合隐私敏感场景
高斯投影——即用随机高斯矩阵预乘数据——是数据科学与机器学习中广泛应用的技术，适用于计算高效优化、编码计算和联邦学习等场景。该操作因内在随机性可提供差分隐私保障。本文从瑞尼差分隐私（RDP）角度重新审视此操作，提出更精细的隐私分析，获得显著更紧的隐私界。进一步证明该改进分析能在线性回归设置中提升性能，并建立理论效用保证。实验表明，所提方法在多个数据集上均实现性能提升，部分情况下还减少运行时间。
原文摘要 · Abstract (English)
Gaussian sketching, which consists of pre-multiplying the data with a random Gaussian matrix, is a widely used technique for multiple problems in data science and machine learning, with applications spanning computationally efficient optimization, coded computing, and federated learning. This operation also provides differential privacy guarantees due to its inherent randomness. In this work, we revisit this operation through the lens of Renyi Differential Privacy (RDP), providing a refined privacy analysis that yields significantly tighter bounds than prior results. We then demonstrate how this improved analysis leads to performance improvement in different linear regression settings, establishing theoretical utility guarantees. Empirically, our methods improve performance across multiple datasets and, in several cases, reduce runtime.
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