Differentially Private Manifold Denoising

Computer Science > Machine Learning [Submitted on 1 Apr 2026] Differentially Private Manifold Denoising Jiaqi Wu, Yiqing Sun, Zhigang Yao We introduce a differentially private manifold denoising framework that allows users to exploit sensitive reference datasets to correct noisy, non-private query points without compromising privacy. The method follows an iterative procedure that (i) privately estimates local means and tangent geometry using the reference data under calibrated sensitivity, (ii) projects query points along the privately estimated subspace toward the local mean via corrective steps at each iteration, and (iii) performs rigorous privacy accounting across iterations and queries using (\varepsilon,\delta)-differential privacy (DP). Conceptually, this framework brings differential privacy to manifold methods, retaining sufficient geometric signal for downstream tasks such as embedding, clustering, and visualization, while providing formal DP guarantees for the reference data. Practically, the procedure is modular and scalable, separating DP-protected local geometry (means and tangents) from budgeted query-point updates, with a simple scheduler allocating privacy budget across iterations and queries. Under standard assumptions on manifold regularity, sampling density, and measurement noise, we establish high-probability utility guarantees showing that corrected queries converge toward the manifold at a non-asymptotic rate governed by sample size, noise level, bandwidth, and the privacy budget. Simulations and case studies demonstrate accurate signal recovery under moderate privacy budgets, illustrating clear utility-privacy trade-offs and providing a deployable DP component for manifold-based workflows in regulated environments without reengineering privacy systems. Comments: 59 pages Subjects: Machine Learning (cs.LG); Cryptography and Security (cs.CR); Statistics Theory (math.ST) Cite as: arXiv:2604.00942 [cs.LG]   (or arXiv:2604.00942v1 [cs.LG] for this version)   https://doi.org/10.48550/arXiv.2604.00942 Focus to learn more Submission history From: Zhigang Yao [view email] [v1] Wed, 1 Apr 2026 14:13:59 UTC (2,909 KB) Access Paper: HTML (experimental) view license Current browse context: cs.LG < prev   |   next > new | recent | 2026-04 Change to browse by: cs cs.CR math math.ST stat stat.TH References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)