Missing Mass for Differentially Private Domain Discovery

2026-03-14

AI Summary

This work addresses the challenge of efficiently outputting a representative subset of items in differential privacy domain discovery, where users hold subsets drawn from an unknown shared domain. The authors propose the Weighted Gaussian Mechanism (WGM) as a core method, establishing for the first time a near-optimal ℓ₁ error bound under Zipf-distributed data and providing a distribution-agnostic ℓ∞ guarantee. Building on these theoretical foundations, WGM is leveraged as a universal preprocessing module to extend existing algorithms—originally designed for known domains—for tasks including set union, top-k selection, and k-hitting set into the unknown-domain setting. Theoretical analysis demonstrates that WGM achieves near-optimal performance across multiple regimes, and empirical evaluations confirm its superiority or competitiveness against current baselines across all three tasks.

Technology Category

• Machine Learning: Privacy
• Search and Optimization: Mixed Discrete/Continuous Search
• Data Mining & Knowledge Management: Anomaly/Outlier Detection

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

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.

Problem

• differentially private domain discovery
• missing mass
• set union
• private top-k
• k-hitting set

Innovation

• Weighted Gaussian Mechanism
• missing mass
• differentially private domain discovery
• unknown domain
• set union