论文标题
差异私有线性回归的假设测试
Hypothesis Testing for Differentially Private Linear Regression
论文作者
论文摘要
在这项工作中，我们针对一般线性模型中的以下问题设计了不同的私有假设测试：测试线性关系并测试混合物的存在。我们的大多数假设检验基于$ f $统计量的差异私有版本，用于一般线性模型框架，在非私人环境中，它们在非私人环境中均无偏见。我们还提供了针对这些问题的其他测试，其中之一是基于Couch，Kazan，Shi，Bray和Groce的差异性非参数测试（CCS 2019），该测试特别适合小型数据集制度。我们表明，差异私有$ f $统计统治与其非私有化对应物的渐近分布收敛。作为推论，差异私有$ f $统计的统计能力会收敛于非私营$ f $统计量的统计能力。通过一套基于蒙特卡洛的实验，我们表明我们的测试达到了所需的显着性水平，并且具有高功率，可以随着我们增加样本大小或隐私性损失参数而接近非私有测试的功能。我们还展示了我们的测试何时在文献中胜过现有方法。
In this work, we design differentially private hypothesis tests for the following problems in the general linear model: testing a linear relationship and testing for the presence of mixtures. The majority of our hypothesis tests are based on differentially private versions of the $F$-statistic for the general linear model framework, which are uniformly most powerful unbiased in the non-private setting. We also present other tests for these problems, one of which is based on the differentially private nonparametric tests of Couch, Kazan, Shi, Bray, and Groce (CCS 2019), which is especially suited for the small dataset regime. We show that the differentially private $F$-statistic converges to the asymptotic distribution of its non-private counterpart. As a corollary, the statistical power of the differentially private $F$-statistic converges to the statistical power of the non-private $F$-statistic. Through a suite of Monte Carlo based experiments, we show that our tests achieve desired significance levels and have a high power that approaches the power of the non-private tests as we increase sample sizes or the privacy-loss parameter. We also show when our tests outperform existing methods in the literature.
