Adaptive Power Iteration Method for Differentially Private PCA

arXiv:2602.11454v3 Announce Type: replace-cross Abstract: We study left(epsilon,eltaright)-differentially private algorithms for the problem of approximately computing the top singular vector of a matrix AinR^{nimes d} where each row of A is a data point in R^{d}. Following Dwork-Talwar-Thakurta-Zhang (STOC 2014), we consider the privacy model where neighboring inputs differ by one single row. We give a novel algorithm that achieves beyond-worst-case guarantees for input matrices with low coherence, which is a structural property of matrices in many applications, including but not limited to i.i.d. data. Our algorithm contributes to the extensive literature on private power iteration methods, where we introduce a new filtering technique which adapts to this coherence parameter. Our work departs from and complements the work by Hardt-Roth (STOC 2013) which achieves beyond-worst-case guarantees for the more restrictive privacy model where neighboring inputs differ in one single entry by at most 1.

Source: arXiv cs.LG | 2026-05-20