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

Ohad Shamir
Proceedings of The 33rd International Conference on Machine Learning, PMLR 48:248-256, 2016.

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 this Paper

BibTeX
@InProceedings{pmlr-v48-shamira16, title = {Fast Stochastic Algorithms for SVD and PCA: Convergence Properties and Convexity}, author = {Shamir, Ohad}, booktitle = {Proceedings of The 33rd International Conference on Machine Learning}, pages = {248--256}, year = {2016}, editor = {Balcan, Maria Florina and Weinberger, Kilian Q.}, volume = {48}, series = {Proceedings of Machine Learning Research}, address = {New York, New York, USA}, month = {20--22 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v48/shamira16.pdf}, url = {https://proceedings.mlr.press/v48/shamira16.html}, 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.} }
Endnote
%0 Conference Paper %T Fast Stochastic Algorithms for SVD and PCA: Convergence Properties and Convexity %A Ohad Shamir %B Proceedings of The 33rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2016 %E Maria Florina Balcan %E Kilian Q. Weinberger %F pmlr-v48-shamira16 %I PMLR %P 248--256 %U https://proceedings.mlr.press/v48/shamira16.html %V 48 %X 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.
RIS
TY - CPAPER TI - Fast Stochastic Algorithms for SVD and PCA: Convergence Properties and Convexity AU - Ohad Shamir BT - Proceedings of The 33rd International Conference on Machine Learning DA - 2016/06/11 ED - Maria Florina Balcan ED - Kilian Q. Weinberger ID - pmlr-v48-shamira16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 48 SP - 248 EP - 256 L1 - http://proceedings.mlr.press/v48/shamira16.pdf UR - https://proceedings.mlr.press/v48/shamira16.html AB - 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. ER -
APA
Shamir, O.. (2016). Fast Stochastic Algorithms for SVD and PCA: Convergence Properties and Convexity. Proceedings of The 33rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 48:248-256 Available from https://proceedings.mlr.press/v48/shamira16.html.

Related Material