Sketch-Flip-Merge: Mergeable Sketches for Private Distinct Counting

TL;DR

This paper introduces the first practical, mergeable, differentially private sketches for distinct counting that combine low error rates with strong privacy guarantees, outperforming existing solutions.

Contribution

It presents a novel randomized algorithm for mergeable, differentially private sketches with optimal estimation, filling a gap in privacy-preserving data summarization.

Findings

Significantly lower empirical errors compared to existing methods

Strong differential privacy guarantees achieved in practical sketches

Outperforms theoretical solutions in simulations and real-world data

Abstract

Data sketching is a critical tool for distinct counting, enabling multisets to be represented by compact summaries that admit fast cardinality estimates. Because sketches may be merged to summarize multiset unions, they are a basic building block in data warehouses. Although many practical sketches for cardinality estimation exist, none provide privacy when merging. We propose the first practical cardinality sketches that are simultaneously mergeable, differentially private (DP), and have low empirical errors. These introduce a novel randomized algorithm for performing logical operations on noisy bits, a tight privacy analysis, and provably optimal estimation. Our sketches dramatically outperform existing theoretical solutions in simulations and on real-world data.