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arXiv · 2210.15178

Anonymized Histograms in Intermediate Privacy Models

Badih Ghazi·Pritish Kamath·Ravi Kumar·Pasin Manurangsi
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Abstract

We study the problem of privately computing the anonymized histogram (a.k.a. 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 $\tilde{O}_\varepsilon(\sqrt{n})$ 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.

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Badih Ghazi, Pritish Kamath, Ravi Kumar, Pasin Manurangsi. 2022-10-27. Anonymized Histograms in Intermediate Privacy Models. https://arxiv.org/abs/2210.15178

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