← Back to all news
arXiv Machine Learning By Anming Gu, Syamantak Kumar, Kevin Tian, Chutong Yang

Gap-Free Streaming PCA Beyond Rank-One Updates: Near-Optimal Rates and Applications to Differential Privacy

Read the original on arXiv Machine Learning →

The paper presents a new analysis of Oja's algorithm for streaming principal component analysis (PCA) that works without any eigengap assumptions, achieving near‑optimal rates and matching lower bounds. It extends the results to a Rayleigh quotient notion of approximate PCA, resolving an open question, and applies the findings to provide gap‑free differentially private PCA guarantees for sub‑Gaussian data. The analysis relies solely on a second‑moment bound of stochastic updates, avoiding the almost‑sure bounds used in previous work.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

Related stories

arXiv Machine Learning
Aug 20

Inference and Uncertainty Quantification for Streaming $r$-PCA

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
More like this →
arXiv Machine Learning
2d ago

Gap-free Differentially Private PCA for Gaussian Data

The paper presents a gap‑free differentially private algorithm for performing principal component analysis on Gaussian data. It addresses the PCA problem while ensuring privacy guarantees without relying on a spectral gap assumption. The work is announced on arXiv with the identifier 2609.31614v1.

By Alina Ene, Huy L. Nguyen
More like this →