Deconvoluting Kernel Density Estimation and Regression for Locally Differentially Private Data

TL;DR

This paper introduces deconvolution techniques for kernel density estimation and regression to accurately analyze locally differentially private data affected by additive noise, improving data utility in privacy-preserving contexts.

Contribution

It develops novel deconvoluting kernel density estimators and regression models tailored for locally differentially private data, addressing the distortion caused by privacy noise.

Findings

Effective density estimation on private data demonstrated

Regression models successfully adapted for noisy privacy-preserving data

Improved accuracy over traditional methods in experiments

Abstract

Local differential privacy has become the gold-standard of privacy literature for gathering or releasing sensitive individual data points in a privacy-preserving manner. However, locally differential data can twist the probability density of the data because of the additive noise used to ensure privacy. In fact, the density of privacy-preserving data (no matter how many samples we gather) is always flatter in comparison with the density function of the original data points due to convolution with privacy-preserving noise density function. The effect is especially more pronounced when using slow-decaying privacy-preserving noises, such as the Laplace noise. This can result in under/over-estimation of the heavy-hitters. This is an important challenge facing social scientists due to the use of differential privacy in the 2020 Census in the United States. In this paper, we develop density estimation methods using smoothing kernels. We use the framework of deconvoluting kernel density estimators to remove the effect of privacy-preserving noise. This approach also allows us to adapt the results from non-parameteric regression with errors-in-variables to develop regression models based on locally differentially private data. We demonstrate the performance of the developed methods on financial and demographic datasets.