naa a22 4500 510809111 CHVBK 20180411083433.0 cr unu---uuuuu 180411e20130601xx s 000 0 eng 10.1007/s12532-013-0053-8 doi (NATIONALLICENCE)springer-10.1007/s12532-013-0053-8 Parallel stochastic gradient algorithms for large-scale matrix completion [Elektronische Daten] [Benjamin Recht, Christopher Ré] 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 4h, while Jellyfish solves the same problem in under 3min on a 12 core workstation. Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society, 2013 Matrix completion nationallicence Incremental gradient methods nationallicence Parallel computing nationallicence Multicore nationallicence Recht Benjamin Computer Sciences Department, University of Wisconsin-Madison, 1210 W Dayton St, 53706, Madison, WI, USA aut Ré Christopher Computer Sciences Department, University of Wisconsin-Madison, 1210 W Dayton St, 53706, Madison, WI, USA aut Mathematical Programming Computation Springer-Verlag 5/2(2013-06-01), 201-226 1867-2949 5:2<201 2013 5 12532 https://doi.org/10.1007/s12532-013-0053-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s12532-013-0053-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Recht Benjamin Computer Sciences Department, University of Wisconsin-Madison, 1210 W Dayton St, 53706, Madison, WI, USA aut NATIONALLICENCE 700 1- Ré Christopher Computer Sciences Department, University of Wisconsin-Madison, 1210 W Dayton St, 53706, Madison, WI, USA aut NATIONALLICENCE 773 0- Mathematical Programming Computation Springer-Verlag 5/2(2013-06-01), 201-226 1867-2949 5:2<201 2013 5 12532 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer