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We address the rectangular matrix completion problem by lifting the unknown matrix to a positive semidefinite matrix in higher dimension, and optimizing a nonconvex objective over the semidefinite factor using a simple gradient descent scheme.
Matrix rank minimization with applications
Maryam Fazel · 2002
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A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization
Samuel Burer and Renato D.C. Monteiro · 2003
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Introductory lectures on convex optimization , volume 87
Yurii Nesterov · 2004
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Maximum-margin matrix factorization
Nathan Srebro, Jason Rennie, and Tommi S Jaakkola · 2004
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Uriel Feige and Eran Ofek · 2005
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Emmanuel J Candès, Xiaodong Li, and Mahdi Soltanolkotabi · 2007
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A direct formulation for sparse pca using semidefinite programming
Alexandre d’Aspremont, Laurent El Ghaoui, Michael I Jordan, and Gert RG Lanckriet · 2007
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Exact matrix completion via convex optimization
Emmanuel J Candès and Benjamin Recht · 2009
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A singular value thresholding algorithm for matrix completion
Jian-Feng Cai, Emmanuel J Candès, and Zuowei Shen · 2010
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The power of convex relaxation: Near-optimal matrix completion
Emmanuel J Candès and Terence Tao · 2010
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Guaranteed rank minimization via singular value projection
Prateek Jain, Raghu Meka, and Inderjit S Dhillon · 2010
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Matrix completion from a few entries
Raghunandan H Keshavan, Andrea Montanari, and Sewoong Oh · 2010
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Practical large-scale optimization for max-norm regularization
Jason D Lee, Ben Recht, Nathan Srebro, Joel Tropp, and Ruslan R Salakhutdinov · 2010
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Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization
Benjamin Recht, Maryam Fazel, and Pablo A Parrilo · 2010
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Estimation of low-rank tensors via convex optimization
Ryota Tomioka, Kohei Hayashi, and Hisashi Kashima · 2010
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Rtrmc: A riemannian trust-region method for low-rank matrix completion
Nicolas Boumal and Pierre-antoine Absil · 2011
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Concentration-based guarantees for low-rank matrix reconstruction
Rina Foygel and Nathan Srebro · 2011
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Solving quadratic equations via phaselift when there are about as many equations as unknowns
Emmanuel J Candès and Xiaodong Li · 2014
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Understanding alternating minimization for matrix completion
Moritz Hardt · 2014
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Fast matrix completion without the condition number
Moritz Hardt and Mary Wootters · 2014
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Dropping convexity for faster semi-definite optimization
Srinadh Bhojanapalli, Anastasios Kyrillidis, and Sujay Sanghavi · 2015
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Incoherence-optimal matrix completion
Yudong Chen · 2015
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A nonconvex optimization framework for low rank matrix estimation
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Low-rank solutions of linear matrix equations via procrustes flow
Stephen Tu, Ross Boczar, Max Simchowitz, Mahdi Soltanolkotabi, and Benjamin Recht · 2016
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