{"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/plan-variance-aware-private-mean-estimation","title":"PLAN: Variance-Aware Private Mean Estimation","arxiv_id":"2306.08745","date":"2023-06-14","proceeding":null,"authors":["Martin Aumüller","Christian Janos Lebeda","Boel Nelson","Rasmus Pagh"],"abstract":"Differentially private mean estimation is an important building block in privacy-preserving algorithms for data analysis and machine learning. Though the trade-off between privacy and utility is well understood in the worst case, many datasets exhibit structure that could potentially be exploited to yield better algorithms. In this paper we present $\\textit{Private Limit Adapted Noise}$ (PLAN), a family of differentially private algorithms for mean estimation in the setting where inputs are independently sampled from a distribution $\\mathcal{D}$ over $\\mathbf{R}^d$, with coordinate-wise standard deviations $\\boldsymbol{\\sigma} \\in \\mathbf{R}^d$. Similar to mean estimation under Mahalanobis distance, PLAN tailors the shape of the noise to the shape of the data, but unlike previous algorithms the privacy budget is spent non-uniformly over the coordinates. Under a concentration assumption on $\\mathcal{D}$, we show how to exploit skew in the vector $\\boldsymbol{\\sigma}$, obtaining a (zero-concentrated) differentially private mean estimate with $\\ell_2$ error proportional to $\\|\\boldsymbol{\\sigma}\\|_1$. Previous work has either not taken $\\boldsymbol{\\sigma}$ into account, or measured error in Mahalanobis distance $\\unicode{x2013}$ in both cases resulting in $\\ell_2$ error proportional to $\\sqrt{d}\\|\\boldsymbol{\\sigma}\\|_2$, which can be up to a factor $\\sqrt{d}$ larger. To verify the effectiveness of PLAN, we empirically evaluate accuracy on both synthetic and real world data.","url_abs":"https://arxiv.org/abs/2306.08745v3","url_pdf":"https://arxiv.org/pdf/2306.08745v3.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":"abstracts"},"code_links":[{"paper_slug":"plan-variance-aware-private-mean-estimation","repo_url":"https://github.com/christianlebeda/plan-experiments","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"privacy-preserving","task_name":"Privacy Preserving"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2306.08745","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2306.08745"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+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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