Score Attack: A Lower Bound Technique for Optimal Differentially Private Learning

[2303.07152] Score Attack: A Lower Bound Technique for Optimal Differentially Private Learning Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Statistics Theory arXiv:2303.07152 (math) [Submitted on 13 Mar 2023 ( v1 ), last revised 15 Aug 2026 (this version, v3)] Title: Score Attack: A Lower Bound Technique for Optimal Differentially Private Learning Authors: T. Tony Cai , Yichen Wang , Linjun Zhang View a PDF of the paper titled Score Attack: A Lower Bound Technique for Optimal Differentially Private Learning, by T. Tony Cai and 2 other authors View PDF HTML (experimental) Abstract: Achieving optimal statistical performance while ensuring the privacy of personal data is a challenging yet crucial objective in modern data analysis. However, characterizing the optimality, particularly the minimax lower bound, under privacy constraints is technically difficult. To address this issue, we propose a novel approach called the score attack, which provides a lower bound on the differential-privacy-constrained minimax risk of parameter estimation. The score attack method is based on the tracing attack concept in differential privacy and can be applied to any statistical model with a well-defined score statistic. It can optimally lower bound the minimax risk of estimating unknown model parameters, up to a logarithmic factor, while ensuring differential privacy for a range of statistical problems. We demonstrate the effectiveness and optimality of this general method in various examples, such as the generalized linear model in both classical and high-dimensional sparse settings, the Bradley-Terry-Luce model for pairwise comparisons, and nonparametric regression over the Sobolev class. Subjects: Statistics Theory (math.ST) ; Cryptography and Security (cs.CR); Machine Learning (cs.LG); Methodology (stat.ME); Machine Learning (stat.ML) Cite as: arXiv:2303.07152 [math.ST] (or arXiv:2303.07152v3 [math.ST] for this version) https://doi.org/10.48550/arXiv.2303.07152 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Yichen Wang [ view email ] [v1] Mon, 13 Mar 2023 14:26:27 UTC (753 KB) [v2] Sat, 12 Jul 2025 21:42:34 UTC (62 KB) [v3] Sat, 15 Aug 2026 05:54:37 UTC (82 KB) Full-text links: Access Paper: View a PDF of the paper titled Score Attack: A Lower Bound Technique for Optimal Differentially Private Learning, by T. Tony Cai and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.ST < prev | next > new | recent | 2023-03 Change to browse by: cs cs.CR cs.LG math stat stat.ME stat.ML stat.TH References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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