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arXiv 2007.05157cs.LGcs.CRstat.MEstat.ML
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差分私有简单线性回归

Differentially Private Simple Linear Regression

Harvard John A. Paulson School of Engineering and Applied Sciences(哈佛大学约翰·A·保尔森工程与应用科学学院);Boston University(波士顿大学);Northeastern University(东北大学)

Daniel Alabi, Audra McMillan, Jayshree Sarathy, Adam Smith, Salil Vadhan

摘要:

经济学和社会科学研究通常需要细粒度地分析敏感个人信息的数据集,模型适合数据的小子集。不幸的是,这种细粒度的分析很容易泄露敏感的个人信息。我们研究简单的线性回归算法,满足差分隐私,一个约束,保证算法的输出几乎没有透露任何个人的输入数据记录,即使是攻击者与任意侧信息的数据集。我们考虑设计的差异隐私算法的简单线性回归的小数据集,数十至数百个数据点,这是一个特别具有挑战性的制度差分隐私。专注于一个特定的应用程序在经济学研究中的小区域分析,我们研究了一系列的算法,我们适应的设置的性能。我们确定了影响其性能的关键因素,通过一系列实验表明,基于鲁棒估计器的算法(特别是Theil-Sen估计器)在最小的数据集上表现良好,但随着数据集大小的增加,其他更标准的算法表现更好。

英文摘要:

Economics and social science research often require analyzing datasets of sensitive personal information at fine granularity, with models fit to small subsets of the data. Unfortunately, such fine-grained analysis can easily reveal sensitive individual information. We study algorithms for simple linear regression that satisfy differential privacy, a constraint which guarantees that an algorithm's output reveals little about any individual input data record, even to an attacker with arbitrary side information about the dataset. We consider the design of differentially private algorithms for simple linear regression for small datasets, with tens to hundreds of datapoints, which is a particularly challenging regime for differential privacy. Focusing on a particular application to small-area analysis in economics research, we study the performance of a spectrum of algorithms we adapt to the setting. We identify key factors that affect their performance, showing through a range of experiments that algorithms based on robust estimators (in particular, the Theil-Sen estimator) perform well on the smallest datasets, but that other more standard algorithms do better as the dataset size increases.

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