Parallel stochastic gradient algorithms for large-scale matrix completion

  • This paper develops Jellyfish, an algorithm for solving data-processing problems with matrix-valued decision variables regularized to have low rank. Particular examples of problems solvable by Jellyfish include matrix completion problems and least-squares problems regularized by the nuclear norm or ?2-norm. Jellyfish implements a projected incremental gradient method with a biased, random ordering of the increments. This biased ordering allows for a parallel implementation that admits a speed-up nearly proportional to the number of processors. On large-scale matrix completion tasks, Jellyfish is orders of magnitude more efficient than existing codes. For example, on the Netflix Prize data set, prior art computes rating predictions in approximately 4 h, while Jellyfish solves the same problem in under 3 min on a 12 core workstation.

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Metadaten
Author:Benjamin Recht, Christopher Ré
DOI:https://doi.org/10.1007/s12532-013-0053-8
ISSN:1867-2949
Parent Title (English):Mathematical Programming Computation
Publisher:Springer Science and Business Media LLC
Document Type:Article
Language:English
Year of Completion:2013
Tag:Software; Theoretical Computer Science
Volume:5
Issue:2
Page Number:26
First Page:201
Last Page:226
Mathematical Programming Computation :MPC 2013 - Issue 2
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