Enhancing Differentially Private Linear Regression via Public Second-Moment

[2508.18037] Enhancing Differentially Private Linear Regression via Public Second-Moment Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Machine Learning arXiv:2508.18037 (cs) [Submitted on 25 Aug 2025 ( v1 ), last revised 15 Aug 2026 (this version, v2)] Title: Enhancing Differentially Private Linear Regression via Public Second-Moment Authors: Zilong Cao (1), Hai Zhang (1) ((1) The School of Mathematics, Northwest University) View a PDF of the paper titled Enhancing Differentially Private Linear Regression via Public Second-Moment, by Zilong Cao (1) and 2 other authors View PDF HTML (experimental) Abstract: Leveraging information from public data has become increasingly crucial in enhancing the utility of differentially private (DP) methods. Traditional DP approaches often require adding noise based solely on private data, which can significantly degrade utility. In this paper, we address this limitation in the context of the ordinary least squares estimator (OLSE) of linear regression based on sufficient statistics perturbation (SSP) under the unbounded data assumption. We propose a novel method that involves transforming private data using the public second-moment matrix to compute a transformed SSP-OLSE, whose second-moment matrix yields a better condition number and improves the OLSE accuracy and robustness. We derive theoretical error bounds about our method and the standard SSP-OLSE to the non-DP OLSE, which reveal the improved robustness and accuracy achieved by our approach. Experiments on synthetic and real-world datasets demonstrate the utility and effectiveness of our method. Subjects: Machine Learning (cs.LG) ; Methodology (stat.ME); Machine Learning (stat.ML) Cite as: arXiv:2508.18037 [cs.LG] (or arXiv:2508.18037v2 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2508.18037 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Zilong Cao [ view email ] [v1] Mon, 25 Aug 2025 13:55:46 UTC (491 KB) [v2] Sat, 15 Aug 2026 04:32:27 UTC (1,109 KB) Full-text links: Access Paper: View a PDF of the paper titled Enhancing Differentially Private Linear Regression via Public Second-Moment, by Zilong Cao (1) and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG < prev | next > new | recent | 2025-08 Change to browse by: cs stat stat.ME stat.ML 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? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) 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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