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Low-rank matrix estimation is a canonical problem that finds numerous applications in signal processing, machine learning and imaging science.
Neural networks and principal component analysis: Learning from examples without local minima
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Cubic regularization of Newton method and its global performance
Y. Nesterov and B. T. Polyak · 2006
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Exact matrix completion via convex optimization
E. J. Candès and B. Recht · 2009
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Guaranteed rank minimization via singular value projection
P. Jain, R. Meka, and I. S. Dhillon · 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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Robust principal component analysis?
E. J. Candès, X. Li, Y. Ma, and J. Wright · 2011
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Tight oracle inequalities for low-rank matrix recovery from a minimal number of noisy random measurements
E. J. Candès and Y. Plan · 2011
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Rank-sparsity incoherence for matrix decomposition
V. Chandrasekaran, S. Sanghavi, P. Parrilo, and A. Willsky · 2011
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Matrix ALPS: Accelerated low rank and sparse matrix reconstruction
A. Kyrillidis and V. Cevher · 2012
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A Riemannian geometry for low-rank matrix completion
B. Mishra, K. A. Apuroop, and R. Sepulchre · 2012
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Low-rank matrix completion using alternating minimization
P. Jain, P. Netrapalli, and S. Sanghavi · 2013
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Robust spectral compressed sensing via structured matrix completion
Y. Chen and Y. Chi · 2014
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Exponential family matrix completion under structural constraints
S. Gunasekar, P. Ravikumar, and J. Ghosh · 2014
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Fast matrix completion without the condition number
M. Hardt and M. Wootters · 2014
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Non-convex robust PCA
P. Netrapalli, U. Niranjan, S. Sanghavi, A. Anandkumar, and P. Jain · 2014
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Incoherence-optimal matrix completion
Y. Chen · 2015
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Phase retrieval via Wirtinger flow: Theory and algorithms
E. Candès, X. Li, and M. Soltanolkotabi · 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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Low rank matrix completion with exponential family noise
J. Lafond · 2015
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Complete dictionary recovery using nonconvex optimization
J. Sun, Q. Qu, and J. Wright · 2015
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A convergent gradient descent algorithm for rank minimization and semidefinite programming from random linear measurements
Q. Zheng and J. Lafferty · 2015
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Dropping convexity for faster semi-definite optimization
S. Bhojanapalli, A. Kyrillidis, and S. Sanghavi · 2016
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Global optimality of local search for low rank matrix recovery
S. Bhojanapalli, B. Neyshabur, and N. Srebro · 2016
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Matrix completion has no spurious local minimum
R. Ge, J. D. Lee, and T. Ma · 2016
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Deep learning without poor local minima
K. Kawaguchi · 2016
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Harnessing structures in big data via guaranteed low-rank matrix estimation: Recent theory and fast algorithms via convex and nonconvex optimization
Y. Chen and Y. Chi · 2018
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Spectral compressed sensing via projected gradient descent
J.-F. Cai, T. Wang, and K. Wei · 2018
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Algorithmic regularization in learning deep homogeneous models: Layers are automatically balanced
S. S. Du, W. Hu, and J. D. Lee · 2018
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The landscape of empirical risk for nonconvex losses
S. Mei, Y. Bai, and A. Montanari · 2018
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Finding low-rank solutions via nonconvex matrix factorization, efficiently and provably
D. Park, A. Kyrillidis, C. Caramanis, and S. Sanghavi · 2018
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A geometric analysis of phase retrieval
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The singular value decomposition and low rank approximation
M. Mazeika · 2016
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Riemannian preconditioning
B. Mishra and R. Sepulchre · 2016
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Guaranteed matrix completion via non-convex factorization
R. Sun and Z.-Q. Luo · 2016
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Low-rank solutions of linear matrix equations via Procrustes flow
S. Tu, R. Boczar, M. Simchowitz, M. Soltanolkotabi, and B. Recht · 2016
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Low rank matrix completion by alternating steepest descent methods
J. Tanner and K. Wei · 2016
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Guarantees of Riemannian optimization for low rank matrix recovery
K. Wei, J.-F. Cai, T. F. Chan, and S. Leung · 2016
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J. Sun, Q. Qu, and J. Wright · 2018
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Global optimality in low-rank matrix optimization
Z. Zhu, Q. Li, G. Tang, and M. B. Wakin · 2018
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Model-free nonconvex matrix completion: Local minima analysis and applications in memory-efficient kernel PCA
J. Chen and X. Li · 2019
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Nonconvex optimization meets low-rank matrix factorization: An overview
Y. Chi, Y. M. Lu, and Y. Chen · 2019
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Rapid, robust, and reliable blind deconvolution via nonconvex optimization
X. Li, S. Ling, T. Strohmer, and K. Wei · 2019
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Implicit regularization in nonconvex statistical estimation: Gradient descent converges linearly for phase retrieval, matrix completion, and blind deconvolution
C. Ma, K. Wang, Y. Chi, and Y. Chen · 2019
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Noisy matrix completion: Understanding statistical guarantees for convex relaxation via nonconvex optimization
Y. Chen, Y. Chi, J. Fan, C. Ma, and Y. Yan · 2020
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Bridging convex and nonconvex optimization in robust PCA: Noise, outliers, and missing data
Y. Chen, J. Fan, C. Ma, and Y. Yan · 2020
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Nonconvex rectangular matrix completion via gradient descent without ℓ 2 , ∞ \ell_{2,\infty} regularization
J. Chen, D. Liu, and X. Li · 2020
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Y. Luo, W. Huang, X. Li, and A. R. Zhang · 2020
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Low-rank matrix recovery with composite optimization: good conditioning and rapid convergence
V. Charisopoulos, Y. Chen, D. Davis, M. Díaz, L. Ding, and D. Drusvyatskiy · 2021
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Nonconvex matrix factorization from rank-one measurements
Y. Li, C. Ma, Y. Chen, and Y. Chi · 2021
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Beyond Procrustes: Balancing-free gradient descent for asymmetric low-rank matrix sensing
C. Ma, Y. Li, and Y. Chi · 2021
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Low-rank matrix recovery with scaled subgradient methods: Fast and robust convergence without the condition number
T. Tong, C. Ma, and Y. Chi · 2021
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Scaling and scalability: Provable nonconvex low-rank tensor estimation from incomplete measurements
T. Tong, C. Ma, A. Prater-Bennette, E. Tripp, and Y. Chi · 2021
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