We study a new privacy model where users belong to certain sensitive groups and we would like to conduct statistical inference on whether there is significant differences in outcomes between the various groups. In particular we do not consider the outcome of users to be sensitive, rather only the membership to certain groups. This is in contrast to previous work that has considered locally private statistical tests, where outcomes and groups are jointly privatized, as well as private A/B testing where the groups are considered public (control and treatment groups) while the outcomes are privatized. We cover several different settings of hypothesis tests after group membership has been privatized amongst the samples, including binary and real valued outcomes. We adopt the generalized $\chi^2$ testing framework used in other works on hypothesis testing in different privacy models, which allows us to cover $Z$-tests, $\chi^2$ tests for independence, t-tests, and ANOVA tests with a single unified approach. When considering two groups, we derive confidence intervals for the true difference in means and show traditional approaches for computing confidence intervals miss the true difference when privacy is introduced. For more than two groups, we consider several mechanisms for privatizing the group membership, showing that we can improve statistical power over the traditional tests that ignore the noise due to privacy. We also consider the application to private A/B testing to determine whether there is a significant change in the difference in means across sensitive groups between the control and treatment.
翻译:我们研究一种新的隐私模式,即用户属于某些敏感群体,我们愿意对不同群体之间结果是否存在重大差异进行统计推断,特别是我们不认为用户的结果敏感,而只是某些群体的成员。这与以前的工作形成对照,以前的工作是考虑当地私人的统计测试,结果和群体联合私有化,以及私人A/B测试,这些群体被视为公共(控制和治疗群体),而结果则私有化。我们研究的是,在群体成员在抽样中私有化后,在包括二进制和真正有价值的结果之后,进行若干不同的假设测试环境。我们采用不同隐私模式中其他假设测试工作中所用的通用的2美元测试框架,这使我们能够涵盖Z-测试、2美元独立测试、t-测试和ANOVA测试。我们在审议两个群体时,对手段上的真正差异产生信任的间隔,并显示在引入隐私时,传统的计算信任间隔期与真正的差异不相称。我们考虑采用两个以上群体在将一些敏感程度机制用于对A类成员实行私有化的过程中,我们还考虑将一些敏感程度机制用于对A类成员实行私有化,我们是否对保密性进行重大测试,从而改进对保密性测试。