In this study, I consider privacy against hypothesis testing adversaries within a non-stochastic framework. He developed a theory of non-stochastic hypothesis testing by borrowing the notion of uncertain variables from non-stochastic information theory. I define tests as binary-valued mappings on uncertain variables and proved a fundamental bound on the best performance of the tests in non-stochastic hypothesis testing. I provide parallels between stochastic and non-stochastic hypothesis-testing frameworks. I use the performance bound in non-stochastic hypothesis testing to develop a measure of privacy. I then construct the reporting policies with the prescribed privacy and utility guarantees. The utility of a reporting policy is measured by the distance between the reported and original values. Finally, I present the notion of indistinguishability as a measure of privacy by extending the identifiability from the privacy literature to the non-stochastic framework. I prove that the linear quantisers can indeed achieve identifiability for responding to linear queries on private datasets.

中文翻译：

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隐私的非随机假设检验

在这项研究中，我考虑了在非随机框架内针对假设检验对手的隐私权。他通过从非随机信息理论中借鉴不确定变量的概念，发展了一种非随机假设检验的理论。我将测试定义为不确定变量的二进制值映射，并证明了在非随机假设测试中测试的最佳性能的基本限制。我提供了随机和非随机假设检验框架之间的相似之处。我使用非随机假设检验中的性能约束来制定隐私度量。然后，我将在规定的隐私权和实用程序保证的基础上构建报告政策。报告策略的效用通过报告值和原始值之间的距离来度量。最后，通过将可识别性从隐私文献扩展到非随机框架，我提出了不可区分性的概念作为隐私的一种度量。我证明线性量化器确实可以实现对私有数据集上线性查询的响应的可识别性。