Non-stochastic hypothesis testing for privacy

Abstract

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.