Towards multi-purpose locally differentially-private synthetic data release via spline wavelet plug-in estimation

TL;DR

This paper introduces a spline wavelet plug-in estimation method for locally differentially private data, enabling the creation of versatile synthetic datasets that support multiple estimation tasks at optimal rates without tailoring privacy mechanisms to specific problems.

Contribution

It develops a novel spline wavelet plug-in estimator for locally private semi-parametric estimation, allowing for multi-purpose synthetic data generation independent of specific functionals.

Findings

Achieves optimal convergence rates for a broad class of functionals.

Enables pre-generated synthetic data usable for various analyses.

Removes the need for tailored privacy mechanisms for different estimation tasks.

Abstract

We develop plug-in estimators for locally differentially private semi-parametric estimation via spline wavelets. The approach leads to optimal rates of convergence for a large class of estimation problems that are characterized by (differentiable) functionals $\Lambda(f)$ of the true data generating density $f$. The crucial feature of the locally private data $Z_1,\dots, Z_n$ we generate is that it does not depend on the particular functional $\Lambda$ (or the unknown density $f$) the analyst wants to estimate. Hence, the synthetic data can be generated and stored a priori and can subsequently be used by any number of analysts to estimate many vastly different functionals of interest at the provably optimal rate. In principle, this removes a long standing practical limitation in statistics of differential privacy, namely, that optimal privacy mechanisms need to be tailored towards the specific estimation problem at hand.