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| Autori principali: | , , |
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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2508.13969 |
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| _version_ | 1866911194652082176 |
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| author | Randrianarisoa, Thibault Steinberger, Lukas Szabó, Botond |
| author_facet | Randrianarisoa, Thibault Steinberger, Lukas Szabó, Botond |
| contents | 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 $Λ(f)$ 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 $Λ$ (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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_13969 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Towards multi-purpose locally differentially-private synthetic data release via spline wavelet plug-in estimation Randrianarisoa, Thibault Steinberger, Lukas Szabó, Botond Statistics Theory 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 $Λ(f)$ 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 $Λ$ (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. |
| title | Towards multi-purpose locally differentially-private synthetic data release via spline wavelet plug-in estimation |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2508.13969 |