Anonymized Histograms in Intermediate Privacy Models

TL;DR

This paper introduces a simple, nearly optimal algorithm for privately computing anonymized histograms in shuffle and pan-private models, enabling accurate estimation of distribution properties under differential privacy.

Contribution

It presents a straightforward algorithm that post-processes Laplace-noised histograms, achieving near-matching error bounds in new privacy models and applications.

Findings

Achieves $ ilde{O}_ ext{ε}(\sqrt{n})$ error in shuffle and pan-private models.

Enables private estimation of entropy, support coverage, and support size.

Simple post-processing approach with broad applicability.

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.