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arXiv · 2508.13969

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

Thibault Randrianarisoa·Lukas Steinberger·Botond Szabó
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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.

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Thibault Randrianarisoa, Lukas Steinberger, Botond Szabó. 2025-08-19. Towards multi-purpose locally differentially-private synthetic data release via spline wavelet plug-in estimation. https://arxiv.org/abs/2508.13969

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