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Recent years have seen a flurry of activities in designing provably efficient nonconvex procedures for solving statistical estimation problems.
The rotation of eigenvectors by a perturbation. iii
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Matrix completion from a few entries
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R. H. Keshavan, A. Montanari, and S. Oh · 2010
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Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization
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A probabilistic and RIPless theory of compressed sensing
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Rank-sparsity incoherence for matrix decomposition
V. Chandrasekaran, S. Sanghavi, P. A. Parrilo, and A. S. Willsky · 2011
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Recovering low-rank matrices from few coefficients in any basis
D. Gross · 2011
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Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion
V. Koltchinskii, K. Lounici, and A. B. Tsybakov · 2011
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Oracle inequalities in empirical risk minimization and sparse recovery problems
V. Koltchinskii · 2011
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A simpler approach to matrix completion
B. Recht · 2011
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A tail inequality for quadratic forms of subgaussian random vectors
D. Hsu, S. M. Kakade, and T. Zhang · 2012
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Restricted strong convexity and weighted matrix completion: optimal bounds with noise
S. Negahban and M. J. Wainwright · 2012
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Concentration and moment inequalities for polynomials of independent random variables
W. Schudy and M. Sviridenko · 2012
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Topics in Random Matrix Theory
T. Tao · 2012
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Introduction to the non-asymptotic analysis of random matrices
R. Vershynin · 2012
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Phase retrieval via matrix completion
E. J. Candès, Y. C. Eldar, T. Strohmer, and V. Voroninski · 2013
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Phaselift: Exact and stable signal recovery from magnitude measurements via convex programming
E. J. Candès, T. Strohmer, and V. Voroninski · 2013
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On robust regression with high-dimensional predictors
N. El Karoui, D. Bean, P. J. Bickel, C. Lim, and B. Yu · 2013
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Low-rank matrix completion using alternating minimization
P. Jain, P. Netrapalli, and S. Sanghavi · 2013
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Phase retrieval using alternating minimization
P. Netrapalli, P. Jain, and S. Sanghavi · 2013
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Hanson-Wright inequality and sub-Gaussian concentration
M. Rudelson and R. Vershynin · 2013
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Blind deconvolution using convex programming
A. Ahmed, B. Recht, and J. Romberg · 2014
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Solving quadratic equations via PhaseLift when there are about as many equations as unknowns
E. J. Candès and X. Li · 2014
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A convex formulation for mixed regression with two components: Minimax optimal rates
Y. Chen, X. Yi, and C. Caramanis · 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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GESPAR: Efficient phase retrieval of sparse signals
Y. Shechtman, A. Beck, and Y. C. Eldar · 2014
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Algorithms and Theory for Clustering and Nonconvex Quadratic Programming
M. Soltanolkotabi · 2014
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Convex optimization: Algorithms and complexity
S. Bubeck · 2015
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Exact and stable covariance estimation from quadratic sampling via convex programming
Y. Chen, Y. Chi, and A. J. Goldsmith · 2015
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Phase retrieval with one or two diffraction patterns by alternating projections with the null initialization
P. Chen, A. Fannjiang, and G.-R. Liu · 2015
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Incoherence-optimal matrix completion
Y. Chen · 2015
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Phase retrieval via Wirtinger flow: Theory and algorithms
E. J. Candès, X. Li, and M. Soltanolkotabi · 2015
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Y. Chen and M. J. Wainwright · 2015
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ROP: Matrix recovery via rank-one projections
T. Cai and A. Zhang · 2015
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On the impact of predictor geometry on the performance on high-dimensional ridge-regularized generalized robust regression estimators
Implicit regularization in matrix factorization
S. Gunasekar, B. E. Woodworth, S. Bhojanapalli, B. Neyshabur, and N. Srebro · 2017
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Phase transitions of spectral initialization for high-dimensional nonconvex estimation
Y. M. Lu and G. Li · 2017
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Blind gain and phase calibration for low-dimensional or sparse signal sensing via power iteration
Y. Li, K. Lee, and Y. Bresler · 2017
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Blind recovery of sparse signals from subsampled convolution
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Fast, robust and non-convex subspace recovery
G. Lerman and T. Maunu · 2017
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The nonconvex geometry of low-rank matrix optimizations with general objective functions
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N. El Karoui · 2015
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Matrix completion and low-rank SVD via fast alternating least squares
T. Hastie, R. Mazumder, J. D. Lee, and R. Zadeh · 2015
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Phase retrieval: An overview of recent developments
K. Jaganathan, Y. C. Eldar, and B. Hassibi · 2015
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Fast exact matrix completion with finite samples
P. Jain and P. Netrapalli · 2015
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Self-calibration and biconvex compressive sensing
S. Ling and T. Strohmer · 2015
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Compressive phase retrieval via generalized approximate message passing
P. Schniter and S. Rangan · 2015
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Convex recovery of a structured signal from independent random linear measurements
J. A. Tropp · 2015
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Q. Li and G. Tang · 2017
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Fundamental limits of weak recovery with applications to phase retrieval
M. Mondelli and A. Montanari · 2017
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Convolutional phase retrieval via gradient descent
Q. Qing, Y. Zhang, Y. Eldar, and J. Wright · 2017
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P. Sur, Y. Chen, and E. J. Candès · 2017
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Complete dictionary recovery over the sphere i: Overview and the geometric picture
J. Sun, Q. Qu, and J. Wright · 2017
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The local convexity of solving systems of quadratic equations
S. Sanghavi, R. Ward, and C. D. White · 2017
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Solving systems of random quadratic equations via truncated amplitude flow
G. Wang, G. B. Giannakis, and Y. C. Eldar · 2017
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Solving most systems of random quadratic equations
G. Wang, G. Giannakis, Y. Saad, and J. Chen · 2017
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Understanding deep learning requires rethinking generalization
C. Zhang, S. Bengio, M. Hardt, B. Recht, and O. Vinyals · 2017
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On the global geometry of sphere-constrained sparse blind deconvolution
Y. Zhang, Y. Lau, H.-w. Kuo, S. Cheung, A. Pasupathy, and J. Wright · 2017
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Recovery guarantees for one-hidden-layer neural networks
K. Zhong, Z. Song, P. Jain, P. L. Bartlett, and I. S. Dhillon · 2017
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A nonconvex approach for phase retrieval: Reshaped wirtinger flow and incremental algorithms
H. Zhang, Y. Zhou, Y. Liang, and Y. Chi · 2017
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The projected power method: An efficient algorithm for joint alignment from pairwise differences
Y. Chen and E. Candès · 2018
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Asymmetry helps: Eigenvalue and eigenvector analyses of asymmetrically perturbed low-rank matrices
Y. Chen, C. Cheng, and J. Fan · 2018
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Nonconvex optimization meets low-rank matrix factorization: An overview
Y. Chi, Y. M. Lu, and Y. Chen · 2018
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Solving (most) of a set of quadratic equalities: Composite optimization for robust phase retrieval
J. C. Duchi and F. Ruan · 2018
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Phasemax: Convex phase retrieval via basis pursuit
T. Goldstein and C. Studer · 2018
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Blind deconvolution by a steepest descent algorithm on a quotient manifold
W. Huang and P. Hand · 2018
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An elementary proof of convex phase retrieval in the natural parameter space via the linear program phasemax
P. Hand and V. Voroninski · 2018
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Debiasing the lasso: Optimal sample size for gaussian designs
A. Javanmard and A. Montanari · 2018
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Rapid, robust, and reliable blind deconvolution via nonconvex optimization
X. Li, S. Ling, T. Strohmer, and K. Wei · 2018
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Nonconvex matrix factorization from rank-one measurements
Y. Li, C. Ma, Y. Chen, and Y. Chi · 2018
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Regularized gradient descent: a non-convex recipe for fast joint blind deconvolution and demixing
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Fast and guaranteed blind multichannel deconvolution under a bilinear system model
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The landscape of empirical risk for nonconvex losses
S. Mei, Y. Bai, and A. Montanari · 2018
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The implicit bias of gradient descent on separable data
D. Soudry, E. Hoffer, M. S. Nacson, S. Gunasekar, and N. Srebro · 2018
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Phase retrieval via randomized kaczmarz: Theoretical guarantees
Y. S. Tan and R. Vershynin · 2018
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Sparse phase retrieval via truncated amplitude flow
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Near-optimal bounds for phase synchronization
Y. Zhong and N. Boumal · 2018
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Branchhull: Convex bilinear inversion from the entrywise product of signals with known signs
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Gradient descent with random initialization: Fast global convergence for nonconvex phase retrieval
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Spectral method and regularized MLE are both optimal for top- K K ranking
Y. Chen, J. Fan, C. Ma, and K. Wang · 2019
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Inference and uncertainty quantification for noisy matrix completion
Y. Chen, J. Fan, C. Ma, and Y. Yan · 2019
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Fast rank-one alternating minimization algorithm for phase retrieval
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A selective overview of deep learning
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A well-tempered landscape for non-convex robust subspace recovery
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Theoretical insights into the optimization landscape of over-parameterized shallow neural networks
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