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Jellyfish

swMATH ID:	12431
Software Authors:	Recht, Benjamin; Ré, Christopher
Description:	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 \(gamma _2\)-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.
Homepage:	http://i.stanford.edu/hazy/hazy/victor/jellyfish/
Keywords:	matrix completion; incremental gradient methods; parallel computing; multicore
Related Software:	SDPLR; softImpute; RTRMC; Saga; ADMiRA; glmnet; HOGWILD; AdaGrad; SPGL1; PRMLT; Manopt; PhaseLift; CoSaMP; LMaFit; MSCRA_rankmin; Pajarito; Gurobi; CRAIG; LSQR; DSCOVR
Cited in:	33 Documents

all top 5

all top 5

4	Mathematical Programming. Series A. Series B
4	SIAM Journal on Optimization
3	Journal of Machine Learning Research (JMLR)
2	Machine Learning
2	SIAM Journal on Scientific Computing
2	Electronic Journal of Statistics
1	Journal of Optimization Theory and Applications
1	Mathematics of Operations Research
1	Operations Research
1	Statistics
1	Journal of Scientific Computing
1	Neural Computation
1	Linear Algebra and its Applications
1	Journal of Mathematical Imaging and Vision
1	Computational Optimization and Applications
1	Combinatorics, Probability and Computing
1	Computational Geosciences
1	Optimization and Engineering
1	The Annals of Applied Statistics
1	Mathematical Programming Computation
1	Journal of the Operations Research Society of China
1	SIAM Journal on Mathematics of Data Science

all top 5

21	Operations research, mathematical programming (90-XX)
15	Numerical analysis (65-XX)
8	Linear and multilinear algebra; matrix theory (15-XX)
7	Statistics (62-XX)
7	Computer science (68-XX)
4	Calculus of variations and optimal control; optimization (49-XX)
3	Probability theory and stochastic processes (60-XX)
1	Combinatorics (05-XX)
1	Algebraic geometry (14-XX)
1	Differential geometry (53-XX)
1	Quantum theory (81-XX)
1	Geophysics (86-XX)
1	Game theory, economics, finance, and other social and behavioral sciences (91-XX)
1	Biology and other natural sciences (92-XX)
1	Systems theory; control (93-XX)