Locally private non-asymptotic testing of discrete distributions is faster using interactive mechanisms
This addresses a privacy-preserving statistical testing challenge for data analysts, but it is incremental as it builds on existing local differential privacy frameworks.
The paper tackles the problem of testing discrete distributions under local differential privacy constraints, showing that interactive mechanisms achieve faster separation rates than non-interactive ones, with optimality proven for cases like uniform and decreasing distributions.
We find separation rates for testing multinomial or more general discrete distributions under the constraint of local differential privacy. We construct efficient randomized algorithms and test procedures, in both the case where only non-interactive privacy mechanisms are allowed and also in the case where all sequentially interactive privacy mechanisms are allowed. The separation rates are faster in the latter case. We prove general information theoretical bounds that allow us to establish the optimality of our algorithms among all pairs of privacy mechanisms and test procedures, in most usual cases. Considered examples include testing uniform, polynomially and exponentially decreasing distributions.