Anonymized Histograms in Intermediate Privacy Models

Badih Ghazi, Pritish Kamath, Ravi Kumar, Pasin Manurangsi

Keywords: differential privacy, shuffle DP, pan privacy, anonymized histograms

TL;DR: Algorithms for anonymized histograms in the shuffle DP and pan privacy models, with error (almost) as in central DP, with applications.

Abstract:

We study the problem of privately computing the $\mbox{\it anonymized histogram}$ (a.k.a. $\mbox{\it unattributed histogram}$), which is defined as the histogram without item labels. Previous works have provided algorithms with $\ell_1$- and $\ell_2^2$-errors of $O_\varepsilon(\sqrt{n})$ in the central model of differential privacy (DP).

In this work, we provide an algorithm with a nearly matching error guarantee of $\widetilde{O}_\varepsilon(\sqrt{n})$ in the shuffle DP and pan-private models. Our algorithm is very simple: it just post-processes the discrete Laplace-noised histogram! Using this algorithm as a subroutine, we show applications in privately estimating symmetric properties of distributions such as entropy, support coverage, and support size.