Online learning of eigenvectors

Dan Garber, Elad E. Hazan, Tengyu Ma

Research output: Chapter in Book/Report/Conference proceedingConference contribution

20 Scopus citations

Abstract

Computing the leading eigenvector of a symmetric real matrix is a fundamental primitive of numerical linear algebra with numerous applications. We consider a natural online extension of the leading eigenvector problem: a sequence of matrices is presented and the goal is to predict for each matrix a unit vector, with the overall goal of competing with the leading eigenvector of the cumulative matrix. Existing regret-minimization algorithms for this problem either require to compute an eigendecompostion every iteration, or suffer from a large dependency of the regret bound on the dimension. In both cases the algorithms are not practical for large scale applications. In this paper we present new algorithms that avoid both issues. On one hand they do not require any expensive matrix decompositions and on the other, they guarantee regret rates with a mild dependence on the dimension at most. In contrast to previous algorithms, our algorithms also admit implementations that enable to leverage sparsity in the data to further reduce computation. We extend our results to also handle non-symmetric matrices.

Original languageEnglish (US)
Title of host publication32nd International Conference on Machine Learning, ICML 2015
EditorsFrancis Bach, David Blei
PublisherInternational Machine Learning Society (IMLS)
Pages560-568
Number of pages9
ISBN (Electronic)9781510810587
StatePublished - Jan 1 2015
Event32nd International Conference on Machine Learning, ICML 2015 - Lile, France
Duration: Jul 6 2015Jul 11 2015

Publication series

Name32nd International Conference on Machine Learning, ICML 2015
Volume1

Other

Other32nd International Conference on Machine Learning, ICML 2015
CountryFrance
CityLile
Period7/6/157/11/15

All Science Journal Classification (ASJC) codes

  • Human-Computer Interaction
  • Computer Science Applications

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