# Robust Streaming PCA

arXiv: https://arxiv.org/abs/1902.03223 · HTML: https://mlsanity.com/paper/1902.03223/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Feb 2019.

## Built on by (most cited first, 6 of 6)

- [Nearly-Linear Time and Streaming Algorithms for Outlier-Robust PCA](https://mlsanity.com/paper/2305.02544/) (2023)
- [Fair Streaming Principal Component Analysis: Statistical and Algorithmic Viewpoint](https://mlsanity.com/paper/2310.18593/) (2023)
- [Implicitly Normalized Online PCA: A Regularized Algorithm with Exact High-Dimensional Dynamics](https://mlsanity.com/paper/2512.01231/) (2025)
- [Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition](https://mlsanity.com/paper/2602.13759/) (2026)
- [Online Supervised Dimension Reduction with Random Features: Diagnostics and Computational Trade-offs](https://mlsanity.com/paper/2609.20454/) (2026)
- [AIM-ZO: Activation-Informed Subspace Maintenance for Zeroth-Order LLM Fine-Tuning](https://mlsanity.com/paper/2609.35257/) (2026)

## Abstract (arXiv)

We consider streaming principal component analysis when the stochastic data generating model is subject to perturbations. While existing models assume a fixed covariance, we adopt a robust perspective where the covariance matrix belongs to a temporal uncertainty set. Under this setting, we provide fundamental limits on convergence of any algorithm recovering principal components. We analyze the convergence of the noisy power method and Oja's algorithm, both studied for the stationary data generating model, and argue that the noisy power method is rate-optimal in our setting. Finally, we demonstrate the validity of our analysis through numerical experiments on synthetic and real-world datasets.