Numerical Estimation of Spatial Distributions under Differential Privacy

TL;DR

This paper introduces a novel method called Disk Area Mechanism (DAM) for estimating spatial distributions under Local Differential Privacy, improving accuracy by projecting spatial data onto a line and optimizing with sliced Wasserstein distance.

Contribution

The paper proposes DAM, a new privacy-preserving spatial distribution estimation technique that leverages numerical domain projection and Wasserstein distance optimization, outperforming existing methods.

Findings

DAM outperforms MDSW in all tested scenarios.

DAM is more accurate than SEM-Geo-I with fine data granularity.

Extensive experiments validate DAM's effectiveness on real and synthetic data.

Abstract

Estimating spatial distributions is important in data analysis, such as traffic flow forecasting and epidemic prevention. To achieve accurate spatial distribution estimation, the analysis needs to collect sufficient user data. However, collecting data directly from individuals could compromise their privacy. Most previous works focused on private distribution estimation for one-dimensional data, which does not consider spatial data relation and leads to poor accuracy for spatial distribution estimation. In this paper, we address the problem of private spatial distribution estimation, where we collect spatial data from individuals and aim to minimize the distance between the actual distribution and estimated one under Local Differential Privacy (LDP). To leverage the numerical nature of the domain, we project spatial data and its relationships onto a one-dimensional distribution. We then use this projection to estimate the overall spatial distribution. Specifically, we propose a reporting mechanism called Disk Area Mechanism (DAM), which projects the spatial domain onto a line and optimizes the estimation using the sliced Wasserstein distance. Through extensive experiments, we show the effectiveness of our DAM approach on both real and synthetic data sets, compared with the state-of-the-art methods, such as Multi-dimensional Square Wave Mechanism (MDSW) and Subset Exponential Mechanism with Geo-I (SEM-Geo-I). Our results show that our DAM always performs better than MDSW and is better than SEM-Geo-I when the data granularity is fine enough.