Debiasing Functions of Private Statistics in Postprocessing
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866918249308880896 |
|---|---|
| author | Calmon, Flavio Du, Elbert Dwork, Cynthia Finley, Brian Franguridi, Grigory |
| author_facet | Calmon, Flavio Du, Elbert Dwork, Cynthia Finley, Brian Franguridi, Grigory |
| contents | Given a differentially private unbiased estimate $\tilde{q}=q(D) +ν$ of a statistic $q(D)$, we wish to obtain unbiased estimates of functions of $q(D)$, such as $1/q(D)$, solely through post-processing of $\tilde{q}$, with no further access to the confidential dataset $D$. To this end, we adapt the deconvolution method used for unbiased estimation in the statistical literature, deriving unbiased estimators for a broad family of twice-differentiable functions when the privacy-preserving noise $ν$ is drawn from the Laplace distribution (Dwork et al., 2006). We further extend this technique to a more general class of functions, deriving approximately optimal estimators that are unbiased for values in a user-specified interval (possibly extending to $\pm \infty$). We use these results to derive an unbiased estimator for private means when the size $n$ of the dataset is not publicly known. In a numerical application, we find that a mechanism that uses our estimator to return an unbiased sample size and mean outperforms a mechanism that instead uses the previously known unbiased privacy mechanism for such means (Kamath et al., 2023). We also apply our estimators to develop unbiased transformation mechanisms for per-record differential privacy, a privacy concept in which the privacy guarantee is a public function of a record's value (Seeman et al., 2024). Our mechanisms provide stronger privacy guarantees than those in prior work (Finley et al., 2024) by using Laplace, rather than Gaussian, noise. Finally, using a different approach, we go beyond Laplace noise by deriving unbiased estimators for polynomials under the weak condition that the noise distribution has sufficiently many moments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_13314 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Debiasing Functions of Private Statistics in Postprocessing Calmon, Flavio Du, Elbert Dwork, Cynthia Finley, Brian Franguridi, Grigory Cryptography and Security Methodology Given a differentially private unbiased estimate $\tilde{q}=q(D) +ν$ of a statistic $q(D)$, we wish to obtain unbiased estimates of functions of $q(D)$, such as $1/q(D)$, solely through post-processing of $\tilde{q}$, with no further access to the confidential dataset $D$. To this end, we adapt the deconvolution method used for unbiased estimation in the statistical literature, deriving unbiased estimators for a broad family of twice-differentiable functions when the privacy-preserving noise $ν$ is drawn from the Laplace distribution (Dwork et al., 2006). We further extend this technique to a more general class of functions, deriving approximately optimal estimators that are unbiased for values in a user-specified interval (possibly extending to $\pm \infty$). We use these results to derive an unbiased estimator for private means when the size $n$ of the dataset is not publicly known. In a numerical application, we find that a mechanism that uses our estimator to return an unbiased sample size and mean outperforms a mechanism that instead uses the previously known unbiased privacy mechanism for such means (Kamath et al., 2023). We also apply our estimators to develop unbiased transformation mechanisms for per-record differential privacy, a privacy concept in which the privacy guarantee is a public function of a record's value (Seeman et al., 2024). Our mechanisms provide stronger privacy guarantees than those in prior work (Finley et al., 2024) by using Laplace, rather than Gaussian, noise. Finally, using a different approach, we go beyond Laplace noise by deriving unbiased estimators for polynomials under the weak condition that the noise distribution has sufficiently many moments. |
| title | Debiasing Functions of Private Statistics in Postprocessing |
| topic | Cryptography and Security Methodology |
| url | https://arxiv.org/abs/2502.13314 |