arXiv:2609.09211v1 Announce Type: new
Abstract: The Davis-Kahan theorem is a fundamental tool in spectral analysis, providing quantitative control over the distance between the eigenspaces of a symme...
By Huan Qing
arXiv:2602. 03682v2 Announce Type: replace-cross Abstract: We analyze the Accelerated Noisy Power Method, an algorithm for Principal Component Analysis in the setting where only inexact matrix-vector products are available, which can arise for instance in decentralized PCA.
By Pierre Agui\'e, Mathieu Even, Laurent Massouli\'e
arXiv:2502.21099v3 Announce Type: replace-cross
Abstract: This paper proposes {\sf AEPG-SPIDER}, an Adaptive Extrapolated Proximal Gradient (AEPG) method with variance reduction for minimizing compos...
By Ganzhao Yuan
arXiv:2609.05718v1 Announce Type: cross
Abstract: We study state tomography when each measurement acts on at most $k$ fresh copies and no quantum memory is retained between blocks. We prove a lower b...
By Ufuk Keskin, Jason Luo, Mahbod Majid, Matthew Radzihovsky
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
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