Fast Stochastic Algorithms for SVD and PCA: Convergence Properties and Convexity

Abstract

We study the convergence properties of the VR-PCA algorithm introduced by (Shamir, 2015) for fast computation of leading singular vectors. We prove several new results, including a formal analysis of a block version of the algorithm, and convergence from random initialization. We also make a few observations of independent interest, such as how pre-initializing with just a single exact power iteration can significantly improve the analysis, and what are the convexity and non-convexity properties of the underlying optimization problem.

Cite

Text

Shamir. "Fast Stochastic Algorithms for SVD and PCA: Convergence Properties and Convexity." International Conference on Machine Learning, 2016.

Markdown

[Shamir. "Fast Stochastic Algorithms for SVD and PCA: Convergence Properties and Convexity." International Conference on Machine Learning, 2016.](https://mlanthology.org/icml/2016/shamir2016icml-fast/)

BibTeX

@inproceedings{shamir2016icml-fast,
  title     = {{Fast Stochastic Algorithms for SVD and PCA: Convergence Properties and Convexity}},
  author    = {Shamir, Ohad},
  booktitle = {International Conference on Machine Learning},
  year      = {2016},
  pages     = {248-256},
  volume    = {48},
  url       = {https://mlanthology.org/icml/2016/shamir2016icml-fast/}
}