Distributed Private Heavy Hitters

TL;DR

This paper develops efficient algorithms and establishes bounds for identifying heavy hitters under differential privacy in a fully distributed setting without a trusted authority, highlighting differences from centralized privacy models.

Contribution

It provides tight bounds and computationally efficient algorithms for heavy hitters with differential privacy in the local distributed model, even with large data universes.

Findings

Tight information-theoretic bounds on accuracy in the local model.

Efficient algorithms for large universe sizes.

Demonstrates separation between local and centralized privacy models.

Abstract

In this paper, we give efficient algorithms and lower bounds for solving the heavy hitters problem while preserving differential privacy in the fully distributed local model. In this model, there are n parties, each of which possesses a single element from a universe of size N. The heavy hitters problem is to find the identity of the most common element shared amongst the n parties. In the local model, there is no trusted database administrator, and so the algorithm must interact with each of the $n$ parties separately, using a differentially private protocol. We give tight information-theoretic upper and lower bounds on the accuracy to which this problem can be solved in the local model (giving a separation between the local model and the more common centralized model of privacy), as well as computationally efficient algorithms even in the case where the data universe N may be exponentially large.