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arXiv 2109.01748cs.CRmath.STstat.TH
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合成数据的保密性:一个统计框架

Privacy of synthetic data: a statistical framework

March Boedihardjo, Thomas Strohmer, Roman Vershynin

摘要:

隐私保护数据分析正在成为一个具有深远影响的挑战性问题。特别是,合成数据是解决数据隐私和数据共享之间的严重冲突的一个有前途的概念。然而,已知准确地生成某些种类的私有合成数据是NP难的。我们开发了一个统计框架差异私人合成数据,这使我们能够规避计算困难的问题。我们认为真实数据是根据某种未知密度从总体Ω中抽取的随机样本。然后,我们用一个更小的随机子集Ω ^* 来代替Ω,我们根据某个已知的密度对它进行采样。通过拟合从真实数据获得的指定线性统计量,我们在缩减空间Omega^* 上生成合成数据。为了确保隐私,我们使用常见的拉普拉斯机制。采用Renyi条件数的概念,它衡量如何以及抽样分布与人口分布的相关性,我们得到明确的界限所提出的方法提供的隐私和准确性。

英文摘要:

Privacy-preserving data analysis is emerging as a challenging problem with far-reaching impact. In particular, synthetic data are a promising concept toward solving the aporetic conflict between data privacy and data sharing. Yet, it is known that accurately generating private, synthetic data of certain kinds is NP-hard. We develop a statistical framework for differentially private synthetic data, which enables us to circumvent the computational hardness of the problem. We consider the true data as a random sample drawn from a population Omega according to some unknown density. We then replace Omega by a much smaller random subset Omega^*, which we sample according to some known density. We generate synthetic data on the reduced space Omega^* by fitting the specified linear statistics obtained from the true data. To ensure privacy we use the common Laplacian mechanism. Employing the concept of Renyi condition number, which measures how well the sampling distribution is correlated with the population distribution, we derive explicit bounds on the privacy and accuracy provided by the proposed method.

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