Frequency Estimation in the Shuffle Model with Almost a Single Message

TL;DR

This paper introduces nearly single-message protocols in the shuffle model of differential privacy for frequency estimation and heavy hitter detection, achieving accuracy close to central DP with minimal communication.

Contribution

It presents the first nearly single-message shuffle-DP protocols for frequency estimation and heavy hitter detection, matching central DP accuracy and improving efficiency.

Findings

Achieves error $ ilde{O}(rac{ ext{polylog}(n)}{n})$ with $1+o(1)$ messages per user.

Designs an efficient heavy hitter detection protocol with $o(1)$ messages per user.

Solves high-dimensional 1-sparse vector summation with optimal error and minimal messages.

Abstract

We present a protocol in the shuffle model of differential privacy (DP) for the \textit{frequency estimation} problem that achieves error $\omega(1)\cdot O(\log n)$, almost matching the central-DP accuracy, with $1+o(1)$ messages per user. This exhibits a sharp transition phenomenon, as there is a lower bound of $\Omega(n^{1/4})$ if each user is allowed to send only one message. Previously, such a result is only known when the domain size $B$ is $o(n)$. For a large domain, we also need an efficient method to identify the \textit{heavy hitters} (i.e., elements that are frequent enough). For this purpose, we design a shuffle-DP protocol that uses $o(1)$ messages per user and can identify all heavy hitters in time polylogarithmic in $B$. Finally, by combining our frequency estimation and the heavy hitter detection protocols, we show how to solve the $B$-dimensional \textit{1-sparse vector summation} problem in the high-dimensional setting $B=\Omega(n)$, achieving the optimal central-DP MSE $\tilde O(n)$ with $1+o(1)$ messages per user. In addition to error and message number, our protocols improve in terms of message size and running time as well. They are also very easy to implement. The experimental results demonstrate order-of-magnitude improvement over prior work.