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arXiv 2402.06137cs.LGcs.CR
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关于带高斯噪声的选择机制的隐私性

On the Privacy of Selection Mechanisms with Gaussian Noise

McGill University(麦吉尔大学);Mila(米拉);Google DeepMind(谷歌DeepMind)

Jonathan Lebensold, Doina Precup, Borja Balle

AI总结:

重新分析带高斯噪声的 Report Noisy Max 和 Above Threshold 机制,在查询有界假设下推导出紧的纯事前和事后 DP 界限,并提出完全自适应的 Gaussian Sparse Vector Technique 机制,实验证明其实用且调参更少。

摘要:

Report Noisy Max 和 Above Threshold 是两种经典的差分隐私(DP)选择机制。它们的输出方式是向一系列低敏感度查询添加噪声,并报告其(带噪声的)答案满足特定条件的查询的身份。当向查询添加 Laplace 噪声时,很容易获得这些机制的纯 DP 保证。另一方面,当使用 Gaussian 噪声实例化时,尽管这些机制的输出位于离散空间中,标准分析仅产生近似 DP 保证。在这项工作中,我们重新审视了对带 Gaussian 噪声的 Report Noisy Max 和 Above Threshold 的分析,并表明,在底层查询是有界的这一额外假设下,可以为 Report Noisy Max 提供纯事前 DP 界限,并为 Above Threshold 提供纯事后 DP 界限。所得界限是紧的,并且依赖于可以通过标准方法进行数值评估的闭式表达式。在经验上,我们发现这些界限在高隐私、低数据机制下能够实现更紧的隐私核算。此外,我们提出了一种简单的隐私过滤器用于组合纯事后 DP 保证,并利用它推导出一种完全自适应的 Gaussian Sparse Vector Technique 机制。最后,我们在移动性和能源消耗数据集上提供了实验,证明我们的 Sparse Vector Technique 在实践中与先前的方法具有竞争力,并且需要更少的超参数调整。

英文摘要:

Report Noisy Max and Above Threshold are two classical differentially private (DP) selection mechanisms. Their output is obtained by adding noise to a sequence of low-sensitivity queries and reporting the identity of the query whose (noisy) answer satisfies a certain condition. Pure DP guarantees for these mechanisms are easy to obtain when Laplace noise is added to the queries. On the other hand, when instantiated using Gaussian noise, standard analyses only yield approximate DP guarantees despite the fact that the outputs of these mechanisms lie in a discrete space. In this work, we revisit the analysis of Report Noisy Max and Above Threshold with Gaussian noise and show that, under the additional assumption that the underlying queries are bounded, it is possible to provide pure ex-ante DP bounds for Report Noisy Max and pure ex-post DP bounds for Above Threshold. The resulting bounds are tight and depend on closed-form expressions that can be numerically evaluated using standard methods. Empirically we find these lead to tighter privacy accounting in the high privacy, low data regime. Further, we propose a simple privacy filter for composing pure ex-post DP guarantees, and use it to derive a fully adaptive Gaussian Sparse Vector Technique mechanism. Finally, we provide experiments on mobility and energy consumption datasets demonstrating that our Sparse Vector Technique is practically competitive with previous approaches and requires less hyper-parameter tuning.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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