Uniformity Testing in the Shuffle Model: Simpler, Better, Faster

Exploring Intermediate Paradigms: A Comparative Analysis of Shuffle and Pan-Private Models in Differential Privacy with Emphasis on Trust Levels, Engineering, and Mathematical Perspectives

“…While this theorem is indeed valuable, tight bounds for a pure shuffle-differential privacy uniformity tester remain scarce to the best of our knowledge. In [19], the authors consider a private-coin, robust shuffle mechanism that achieves a sample complexity 𝑚 = 𝑂( The key insight from this section relates to the sample complexities' relative ordering. As we progress from the local to central models, we observe an enhancement in sample complexity with respect to k. Nevertheless, it's essential to acknowledge the paper's overarching theme, which underscores the overlap of these paradigms.…”

Topics and Techniques in Distribution Testing

“…Turning to shuffle privacy, the algorithm behind Theorem 1.3 starts with the following observation, which was somewhat implicit in [CL22] in the context of uniformity testing: if n users get each a sample from some distribution p over [k] and use the distributed Poisson mechanism with parameter µ n = O 1/(nε 2 ) to "privately report" their data in the shuffle model, then the central server gets access to N := n + kµ i.i.d. samples from a new mixture distribution…”

“…We note that a natural idea to obtain a (different) private-coin shuffle private algorithm (and, via domain compression, a corresponding-public-coin one as well) would be to start from a locally private algorithm under heterogeneous privacy constraints and apply the amplification by shuffling result of [FMT21]. This idea was used in [CL22] for identity testing (under homogeneous privacy constraints), i.e., testing whether an unknown distribution is equal to a fully known reference one. However, this approach comes with two conditions on the LDP protocol one starts with: (1) all users of the same group must use the same local randomizer, and (2) the protocol needs to work reasonably well even for large privacy parameters ε 1 , ε 2 ≫ 1, i.e., in the low-privacy regime.…”

“…However, this approach comes with two conditions on the LDP protocol one starts with: (1) all users of the same group must use the same local randomizer, and (2) the protocol needs to work reasonably well even for large privacy parameters ε 1 , ε 2 ≫ 1, i.e., in the low-privacy regime. Unfortunately, the LDP protocol behind Theorem 1.1 satisfies (1) but not (2), and thus amplification by shuffling would not lead to a shuffle private algorithm with good enough sample complexity; and the LDP identity testing algorithm of [CL22] does not seem to generalize to closeness testing, let alone closeness testing under heterogeneous privacy constraints. We believe that obtaining a sample-optimal LDP algorithm under heterogeneous privacy constraints satisfying (1) and (2) could lead to an improvement over Theorem 1.3 and Corollary 1.4 (in terms of n 2 ), and leave this as an interesting future direction.…”