Answering Multi-Dimensional Range Queries under Local Differential Privacy

TL;DR

This paper presents a novel approach called Hybrid-Dimensional Grids (HDG) for answering multi-dimensional range queries under local differential privacy, effectively balancing correlation capture, dimensionality, and attribute domain size.

Contribution

It introduces HDG, combining 1-D and 2-D grids, with guidelines for grid granularity to improve accuracy in privacy-preserving range query answering.

Findings

HDG significantly outperforms existing methods in accuracy.

The approach effectively balances privacy, accuracy, and computational efficiency.

Experimental results validate the effectiveness of HDG on real and synthetic datasets.

Abstract

In this paper, we tackle the problem of answering multi-dimensional range queries under local differential privacy. There are three key technical challenges: capturing the correlations among attributes, avoiding the curse of dimensionality, and dealing with the large domains of attributes. None of the existing approaches satisfactorily deals with all three challenges. Overcoming these three challenges, we first propose an approach called Two-Dimensional Grids (TDG). Its main idea is to carefully use binning to partition the two-dimensional (2-D) domains of all attribute pairs into 2-D grids that can answer all 2-D range queries and then estimate the answer of a higher dimensional range query from the answers of the associated 2-D range queries. However, in order to reduce errors due to noises, coarse granularities are needed for each attribute in 2-D grids, losing fine-grained distribution information for individual attributes. To correct this deficiency, we further propose Hybrid-Dimensional Grids (HDG), which also introduces 1-D grids to capture finer-grained information on distribution of each individual attribute and combines information from 1-D and 2-D grids to answer range queries. To make HDG consistently effective, we provide a guideline for properly choosing granularities of grids based on an analysis of how different sources of errors are impacted by these choices. Extensive experiments conducted on real and synthetic datasets show that HDG can give a significant improvement over the existing approaches.