Differentially Private High-Dimensional Approximate Range Counting, Revisited

TL;DR

This paper introduces a simple, tunable data structure for differentially private approximate near neighbor counting, improving utility and efficiency over recent methods by leveraging locality sensitive filters and extreme value theory.

Contribution

It develops a new differentially private data structure for ANNC based on locality sensitive filters, with improved utility and efficiency, and clarifies the connection between ANN and DP-ANNC.

Findings

Achieves comparable performance to recent state-of-the-art methods

Offers better utility at higher space and query costs

Provides a more efficient algorithm under pure ε-DP

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).