{"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/lightweight-protocols-for-distributed-private","title":"Lightweight Protocols for Distributed Private Quantile Estimation","arxiv_id":"2502.02990","date":"2025-02-05","proceeding":null,"authors":["Anders Aamand","Fabrizio Boninsegna","Abigail Gentle","Jacob Imola","Rasmus Pagh"],"abstract":"Distributed data analysis is a large and growing field driven by a massive proliferation of user devices, and by privacy concerns surrounding the centralised storage of data. We consider two \\emph{adaptive} algorithms for estimating one quantile (e.g.~the median) when each user holds a single data point lying in a domain $[B]$ that can be queried once through a private mechanism; one under local differential privacy (LDP) and another for shuffle differential privacy (shuffle-DP). In the adaptive setting we present an $\\varepsilon$-LDP algorithm which can estimate any quantile within error $\\alpha$ only requiring $O(\\frac{\\log B}{\\varepsilon^2\\alpha^2})$ users, and an $(\\varepsilon,\\delta)$-shuffle DP algorithm requiring only $\\widetilde{O}((\\frac{1}{\\varepsilon^2}+\\frac{1}{\\alpha^2})\\log B)$ users. Prior (nonadaptive) algorithms require more users by several logarithmic factors in $B$. We further provide a matching lower bound for adaptive protocols, showing that our LDP algorithm is optimal in the low-$\\varepsilon$ regime. Additionally, we establish lower bounds against non-adaptive protocols which paired with our understanding of the adaptive case, proves a fundamental separation between these models.","url_abs":"https://arxiv.org/abs/2502.02990v1","url_pdf":"https://arxiv.org/pdf/2502.02990v1.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":"lightweight-protocols-for-distributed-private","repo_url":"https://github.com/NynsenFaber/Quantile_estimation_with_adaptive_LDP","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2502.02990","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}