Fast Stochastic Algorithms for SVD and PCA: Convergence Properties and Convexity
Machine Learning
2015-08-03 v1 Numerical Analysis
Numerical Analysis
Optimization and Control
Machine Learning
Abstract
We study the convergence properties of the VR-PCA algorithm introduced by \cite{shamir2015stochastic} 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 runtime of stochastic methods, and what are the convexity and non-convexity properties of the underlying optimization problem.
Cite
@article{arxiv.1507.08788,
title = {Fast Stochastic Algorithms for SVD and PCA: Convergence Properties and Convexity},
author = {Ohad Shamir},
journal= {arXiv preprint arXiv:1507.08788},
year = {2015}
}
Comments
35 pages, 2 figures