Missing Mass for Differentially Private Domain Discovery

TL;DR

This paper introduces the Weighted Gaussian Mechanism (WGM) for differentially private domain discovery, providing near-optimal guarantees and improving utility in private top-k and hitting set problems through theoretical analysis and experiments.

Contribution

The paper proposes WGM as a simple, effective method with near-optimal guarantees for private domain discovery and extends its application to improve existing algorithms for unknown domain problems.

Findings

WGM achieves near-optimal missing mass guarantees on Zipfian data.

WGM-based methods outperform existing baselines in experiments.

New utility guarantees for private top-k and hitting set with unknown domains.

Abstract

We study several problems in differentially private domain discovery, where each user holds a subset of items from a shared but unknown domain, and the goal is to output an informative subset of items. For set union, we show that the simple baseline Weighted Gaussian Mechanism (WGM) has a near-optimal $\ell_1$ missing mass guarantee on Zipfian data as well as a distribution-free $\ell_\infty$ missing mass guarantee. We then apply the WGM as a domain-discovery precursor for existing known-domain algorithms for private top-$k$ and $k$-hitting set and obtain new utility guarantees for their unknown domain variants. Finally, experiments demonstrate that all of our WGM-based methods are competitive with or outperform existing baselines for all three problems.