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...

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Bibliographic Details
Published in:Mathematical programming computation Vol. 5; no. 2; pp. 201 - 226
Main Authors: Recht, Benjamin, Ré, Christopher
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer-Verlag 01.06.2013
Subjects:
Full Length Paper
Mathematics
Mathematics and Statistics
Mathematics of Computing
Operations Research/Decision Theory
Optimization
Theory of Computation
Multicore
Parallel computing
90C25
Incremental gradient methods
90C06
90C15
Matrix completion
ISSN:1867-2949, 1867-2957
Online Access:Get full text
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Summary: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 -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.
ISSN:1867-2949
1867-2957
DOI:10.1007/s12532-013-0053-8