{"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/differentially-private-quantiles-with-smaller","title":"Differentially Private Quantiles with Smaller Error","arxiv_id":"2505.13662","date":"2025-05-19","proceeding":null,"authors":["Jacob Imola","Fabrizio Boninsegna","Hannah Keller","Anders Aamand","Amrita Roy Chowdhury","Rasmus Pagh"],"abstract":"In the approximate quantiles problem, the goal is to output $m$ quantile estimates, the ranks of which are as close as possible to $m$ given quantiles $0 \\leq q_1 \\leq\\dots \\leq q_m \\leq 1$. We present a mechanism for approximate quantiles that satisfies $\\varepsilon$-differential privacy for a dataset of $n$ real numbers where the ratio between the distance between the closest pair of points and the size of the domain is bounded by $\\psi$. As long as the minimum gap between quantiles is sufficiently large, $|q_i-q_{i-1}|\\geq \\Omega\\left(\\frac{m\\log(m)\\log(\\psi)}{n\\varepsilon}\\right)$ for all $i$, the maximum rank error of our mechanism is $O\\left(\\frac{\\log(\\psi) + \\log^2(m)}{\\varepsilon}\\right)$ with high probability. Previously, the best known algorithm under pure DP was due to Kaplan, Schnapp, and Stemmer~(ICML '22), who achieved a bound of $O\\left(\\frac{\\log(\\psi)\\log^2(m) + \\log^3(m)}{\\varepsilon}\\right)$. Our improvement stems from the use of continual counting techniques which allows the quantiles to be randomized in a correlated manner. We also present an $(\\varepsilon,\\delta)$-differentially private mechanism that relaxes the gap assumption without affecting the error bound, improving on existing methods when $\\delta$ is sufficiently close to zero. We provide experimental evaluation which confirms that our mechanism performs favorably compared to prior work in practice, in particular when the number of quantiles $m$ is large.","url_abs":"https://arxiv.org/abs/2505.13662v1","url_pdf":"https://arxiv.org/pdf/2505.13662v1.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":"differentially-private-quantiles-with-smaller","repo_url":"https://github.com/nynsenfaber/dp_cc_quantiles","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2505.13662","atlas_url":"https://app.syntology.ai/?focus=2505.13662","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2505.13662"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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