Locally Private Hypothesis Testing

We initiate the study of differentially private hypothesis testing in the local-model, under both the standard (symmetric) randomized-response mechanism [War65, KLN08] and the newer (non-symmetric) mechanisms [BS15, BNST17]. First, we study the general framework of mapping each user’s type into a signal and show that the problem of finding the maximumlikelihood distribution over the signals is feasible. Then we discuss the randomized-response mechanism and show that, in essence, it maps the nulland alternative-hypotheses onto new sets, an affine translation of the original sets. We then give sample complexity bounds for identity and independence testing under randomized-response. We then move to the newer nonsymmetric mechanisms and show that there too the problem of finding the maximum-likelihood distribution is feasible. Under the mechanism of Bassily et al [BNST17] we give identity and independence testers with better sample complexity than the testers in the symmetric case, and we also propose a χ-based identity tester which we investigate empirically.