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We show that there are no spurious local minima in the non-convex factorized parametrization of low-rank matrix recovery from incoherent linear measurements.
A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization
S. Burer and R. D. Monteiro · 2003
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Weighted low-rank approximations
N. Srebro and T. Jaakkola · 2003
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Local minima and convergence in low-rank semidefinite programming
S. Burer and R. D. Monteiro · 2005
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Fast maximum margin matrix factorization for collaborative prediction
J. D. Rennie and N. Srebro · 2005
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Cubic regularization of newton method and its global performance
Y. Nesterov and B. T. Polyak · 2006
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The restricted isometry property and its implications for compressed sensing
E. J. Candès · 2008
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Quantum state tomography via compressed sensing
D. Gross, Y.-K. Liu, S. T. Flammia, S. Becker, and J. Eisert · 2010
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Guaranteed rank minimization via singular value projection
P. Jain, R. Meka, and I. S. Dhillon · 2010
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Low-rank optimization on the cone of positive semidefinite matrices
M. Journée, F. Bach, P.-A. Absil, and R. Sepulchre · 2010
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Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization
B. Recht, M. Fazel, and P. A. Parrilo · 2010
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Tight oracle inequalities for low-rank matrix recovery from a minimal number of noisy random measurements
E. J. Candes and Y. Plan · 2011
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Complexity bounds for second-order optimality in unconstrained optimization
C. Cartis, N. I. Gould, and P. L. Toint · 2012
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Quantum tomography via compressed sensing: Error bounds, sample complexity and efficient estimators
S. Flammia, D. Gross, Y.-K. Liu, and J. Eisert · 2012
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Efficient algorithms for collaborative filtering
R. H. Keshavan · 2012
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Low-rank matrix completion using alternating minimization
P. Jain, P. Netrapalli, and S. Sanghavi · 2013
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Computational limits for matrix completion
M. Hardt, R. Meka, P. Raghavendra, and B. Weitz · 2014
Global convergence of stochastic gradient descent for some non-convex matrix problems
C. D. Sa, C. Re, and K. Olukotun · 2015
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Complete dictionary recovery using nonconvex optimization
J. Sun, Q. Qu, and J. Wright · 2015
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Low-rank solutions of linear matrix equations via Procrustes flow
S. Tu, R. Boczar, M. Soltanolkotabi, and B. Recht · 2015
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Global convergence of a grassmannian gradient descent algorithm for subspace estimation
D. Zhang and L. Balzano · 2015
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A nonconvex optimization framework for low rank matrix estimation
T. Zhao, Z. Wang, and H. Liu · 2015
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Large-scale multi-label learning with missing labels
H.-F. Yu, P. Jain, P. Kar, and I. Dhillon · 2014
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Dropping convexity for faster semi-definite optimization
S. Bhojanapalli, A. Kyrillidis, and S. Sanghavi · 2015
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Y. Chen and M. J. Wainwright · 2015
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Escaping from saddle points—online stochastic gradient for tensor decomposition
R. Ge, F. Huang, C. Jin, and Y. Yuan · 2015
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Q. Zheng and J. Lafferty · 2015
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A. S. Bandeira, N. Boumal, and V. Voroninski · 2016
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Matrix completion has no spurious local minimum
R. Ge, J. Lee, and T. Ma · 2016
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A grothendieck-type inequality for local maxima
A. Montanari · 2016
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A geometric analysis of phase retrieval
J. Sun, Q. Qu, and J. Wright · 2016
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