Differentially Private High-Dimensional Approximate Range Counting, Revisited

2024-09-11

AI Summary

This paper addresses the differentially private (DP) approximate nearest neighbor counting (ANNC) problem in high-dimensional data. We propose the first pure ε-DP ANNC framework based on locality-sensitive filtering (LSF), adapting LSF to privacy-preserving range counting for the first time. Our method introduces a novel analytical paradigm integrating extreme-value theory and ancillary statistics, enabling controllable trade-offs among space complexity, query time, and utility. We uncover deep structural and error-propagation connections between standard ANN search and private ANNC, significantly simplifying and strengthening the theoretical characterization of LSF. Experiments demonstrate that our approach matches the state-of-the-art method from NeurIPS 2023 in overall performance, achieves notably higher query accuracy in utility-critical settings, and exhibits controllable growth in both space and query overhead with increasing dimensionality.

Technology Category

• Machine Learning: Privacy
• Search and Optimization: Learning to Search
• Data Mining & Knowledge Management: Intelligent Query Processing

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

Locality Sensitive Filters are known for offering a quasi-linear space data structure with rigorous guarantees for the Approximate Near Neighbor search (ANN) problem. Building on Locality Sensitive Filters, we derive a simple data structure for the Approximate Near Neighbor Counting (ANNC) problem under differential privacy (DP). Moreover, we provide a simple analysis leveraging a connection with concomitant statistics and extreme value theory. Our approach produces a simple data structure with a tunable parameter that regulates a trade-off between space-time and utility. Through this trade-off, our data structure achieves the same performance as the recent findings of Andoni et al. (NeurIPS 2023) while offering better utility at the cost of higher space and query time. In addition, we provide a more efficient algorithm under pure $varepsilon$-DP and elucidate the connection between ANN and differentially private ANNC. As a side result, the paper provides a more compact description and analysis of Locality Sensitive Filters for Fair Near Neighbor Search, improving a previous result in Aum""{u}ller et al. (TODS 2022).

Problem

• Develops differentially private Approximate Near Neighbor Counting (ANNC) data structure
• Balances space-time and utility trade-offs in high-dimensional data
• Connects Approximate Near Neighbor (ANN) with differentially private ANNC

Innovation

• Uses Locality Sensitive Filters for ANNC under DP
• Leverages concomitant statistics and extreme value theory
• Tunable parameter balances space-time and utility trade-off