Nearly-Linear Time and Streaming Algorithms for Outlier-Robust PCA
Abstract
We study principal component analysis (PCA), where given a dataset in $\mathbb R^d$ from a distribution, the task is to find a unit vector $v$ that approximately maximizes the variance of the distribution after being projected along $v$. Despite being a classical task, standard estimators fail drastically if the data contains even a small fraction of outliers, motivating the problem of robust PCA. Recent work has developed computationally-efficient algorithms for robust PCA that either take super-linear time or have sub-optimal error guarantees. Our main contribution is to develop a nearly linear time algorithm for robust PCA with near-optimal error guarantees. We also develop a single-pass streaming algorithm for robust PCA with memory usage nearly-linear in the dimension.
Cite
Text
Diakonikolas et al. "Nearly-Linear Time and Streaming Algorithms for Outlier-Robust PCA." International Conference on Machine Learning, 2023.Markdown
[Diakonikolas et al. "Nearly-Linear Time and Streaming Algorithms for Outlier-Robust PCA." International Conference on Machine Learning, 2023.](https://mlanthology.org/icml/2023/diakonikolas2023icml-nearlylinear/)BibTeX
@inproceedings{diakonikolas2023icml-nearlylinear,
title = {{Nearly-Linear Time and Streaming Algorithms for Outlier-Robust PCA}},
author = {Diakonikolas, Ilias and Kane, Daniel and Pensia, Ankit and Pittas, Thanasis},
booktitle = {International Conference on Machine Learning},
year = {2023},
pages = {7886-7921},
volume = {202},
url = {https://mlanthology.org/icml/2023/diakonikolas2023icml-nearlylinear/}
}