Estimating Numerical Distributions under Local Differential Privacy

TL;DR

This paper introduces a novel reporting mechanism and an estimation algorithm for recovering numerical distributions under local differential privacy, outperforming existing methods in utility.

Contribution

The paper presents the square wave (SW) mechanism and EMS algorithm, leveraging the numerical domain for improved privacy-utility trade-offs in distribution estimation.

Findings

SW with EMS outperforms other methods in utility metrics

The approach effectively exploits numerical domain properties

Extensive experiments validate the method's superiority

Abstract

When collecting information, local differential privacy (LDP) relieves the concern of privacy leakage from users' perspective, as user's private information is randomized before sent to the aggregator. We study the problem of recovering the distribution over a numerical domain while satisfying LDP. While one can discretize a numerical domain and then apply the protocols developed for categorical domains, we show that taking advantage of the numerical nature of the domain results in better trade-off of privacy and utility. We introduce a new reporting mechanism, called the square wave SW mechanism, which exploits the numerical nature in reporting. We also develop an Expectation Maximization with Smoothing (EMS) algorithm, which is applied to aggregated histograms from the SW mechanism to estimate the original distributions. Extensive experiments demonstrate that our proposed approach, SW with EMS, consistently outperforms other methods in a variety of utility metrics.