[2604.00942] Differentially Private Manifold Denoising

Computer Science > Machine Learning arXiv:2604.00942 (cs) [Submitted on 1 Apr 2026] Title:Differentially Private Manifold Denoising Authors:Jiaqi Wu, Yiqing Sun, Zhigang Yao View a PDF of the paper titled Differentially Private Manifold Denoising, by Jiaqi Wu and 1 other authors View PDF HTML (experimental) Abstract: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 ...