The paper tackles two key gaps in streaming PCA using Oja's algorithm: it establishes sharp operator‑norm convergence for general‑rank subspaces under sub‑Gaussian data, and it provides distributional inference for the resulting subspace estimator. The authors remove non‑vanishing remainder terms from existing analyses, achieving rates that match minimax bounds in both dense‑tail and sparse‑tail regimes. They further develop a linearization of Oja’s iterates, enabling high‑dimensional Gaussian approximations and an online multiplier bootstrap for practical inference.
By Haoshu Xu, Hongzhe Li
SuperPCA is a new algorithm for high‑dimensional principal component analysis that exploits an approximate eigenspace of the sample covariance matrix. The authors show that the subspace spanned by several leading eigenvectors contains useful signal information long before individual eigenvectors converge, and they derive posteriori bounds on the angle between this subspace and the true signal subspace. By using only a small number of subsampled coordinates, SuperPCA can achieve up to a ten‑fold improvement in accuracy over classical PCA while reducing data acquisition costs, especially when the signals are approximately sparse.
By Irina-Beatrice Haas, Maike Meier, Yuji Nakatsukasa, Taejun Park
arXiv:2602. 02190v2 Announce Type: replace-cross Abstract: A common approach to perform PCA on probability measures is to embed them into a Hilbert space where standard functional PCA techniques apply.
By Gachon Erell, J\'er\'emie Bigot, Elsa Cazelles
arXiv:2609.05796v1 Announce Type: cross
Abstract: Principal component analysis (PCA) can rotate away from its population target when a covariance matrix is estimated from limited data. We introduce d...
By Qiang Sun
The paper studies streaming principal component analysis under a robust setting where the covariance matrix can vary within a temporal uncertainty set, rather than being fixed. It establishes fundamental convergence limits for any algorithm that recovers principal components and analyzes the noisy power method and Oja's algorithm, showing that the noisy power method achieves rate‑optimal convergence in this setting. Numerical experiments on synthetic and real‑world data confirm the theoretical findings.
By Daniel Bienstock, Minchan Jeong, Apurv Shukla, Se-Young Yun
arXiv:2606. 14533v1 Announce Type: new Abstract: Principal Component Analysis (PCA) preserves variance, not the information needed to detect rare catastrophic events.
By Hamidou Tembine