Inference Under Information Constraints III: Local Privacy Constraints

We study goodness-of-fit and independence testing of discrete distributions in a setting where samples are distributed across multiple users. The users wish to preserve the privacy their data while enabling central server perform tests. Under notion local differential privacy, we propose simple, sample-optimal, communication-efficient protocols for these two questions noninteractive setting, addition may or not share common random seed. In particular, show that availability shared (public) randomness greatly reduces sample complexity. Underlying our public-coin privacy-preserving mappings which, when applied samples, minimally contract distance between respective probability distributions.