{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/debiasing-functions-of-private-statistics-in","title":"Debiasing Functions of Private Statistics in Postprocessing","arxiv_id":"2502.13314","date":"2025-02-18","proceeding":null,"authors":["Flavio Calmon","Elbert Du","Cynthia Dwork","Brian Finley","Grigory Franguridi"],"abstract":"Given a differentially private unbiased estimate $\\tilde{q}=q(D) +\\nu$ 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 $\\nu$ 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.","url_abs":"https://arxiv.org/abs/2502.13314v4","url_pdf":"https://arxiv.org/pdf/2502.13314v4.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"debiasing-functions-of-private-statistics-in","repo_url":"https://github.com/franguridi/debiased-dp","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}