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We study a noisy tensor completion problem of broad practical interest, namely, the reconstruction of a low-rank tensor from highly incomplete and randomly corrupted observations of its entries.
Brainweb: Online interface to a 3d mri simulated brain database
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Orthogonal tensor decompositions
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E. Candès and B. Recht · 2009
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T. G. Kolda and B. W. Bader · 2009
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R. H. Keshavan, A. Montanari, and S. Oh · 2010
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Matrix completion from noisy entries
R. H. Keshavan, A. Montanari, and S. Oh · 2010
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Estimation of low-rank tensors via convex optimization
R. Tomioka, K. Hayashi, and H. Kashima · 2010
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Introduction to the non-asymptotic analysis of random matrices
R. Vershynin · 2010
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Recovering low-rank matrices from few coefficients in any basis
D. Gross · 2011
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Tensor completion and low- n n -rank tensor recovery via convex optimization
S. Gandy, B. Recht, and I. Yamada · 2011
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Oracle inequalities in empirical risk minimization and sparse recovery problems
V. Koltchinskii · 2011
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5D and 4D pre-stack seismic data completion using tensor nuclear norm (TNN)
G. Ely, S. Aeron, N. Hao, and M. E. Kilmer · 2013
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Most tensor problems are np-hard
C. J. Hillar and L.-H. Lim · 2013
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Third-order tensors as operators on matrices: A theoretical and computational framework with applications in imaging
M. E. Kilmer, K. Braman, N. Hao, and R. C. Hoover · 2013
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Robust and sparse estimation of tensor decompositions
H.-J. Kim, E. Ollila, V. Koivunen, and C. Croux · 2013
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Low-rank matrix and tensor completion via adaptive sampling
A. Krishnamurthy and A. Singh · 2013
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Tensor completion based on nuclear norm minimization for 5d seismic data reconstruction
N. Kreimer, A. Stanton, and M. D. Sacchi · 2013
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Tensor completion for estimating missing values in visual data
J. Liu, P. Musialski, P. Wonka, and J. Ye · 2013
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A new convex relaxation for tensor completion
B. Romera-Paredes and M. Pontil · 2013
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A block coordinate descent method for regularized multiconvex optimization with applications to nonnegative tensor factorization and completion
Y. Xu and W. Yin · 2013
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Tensor decompositions for learning latent variable models
A. Anandkumar, R. Ge, D. Hsu, S. M. Kakade, and M. Telgarsky · 2014
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Guaranteed non-orthogonal tensor decomposition via alternating rank- 1 1 updates
A. Anandkumar, R. Ge, and M. Janzamin · 2014
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Robust spectral compressed sensing via structured matrix completion
Y. Chen and Y. Chi · 2014
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Robust low-rank tensor recovery: Models and algorithms
D. Goldfarb and Z. Qin · 2014
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Provable tensor factorization with missing data
P. Jain and S. Oh · 2014
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High-dimensional covariance matrix estimation with missing observations
K. Lounici · 2014
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Factor matrix trace norm minimization for low-rank tensor completion
Y. Liu, F. Shang, H. Cheng, J. Cheng, and H. Tong · 2014
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Square deal: Lower bounds and improved relaxations for tensor recovery
C. Mu, B. Huang, J. Wright, and D. Goldfarb · 2014
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A statistical model for tensor PCA
E. Richard and A. Montanari · 2014
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Tensor-based formulation and nuclear norm regularization for multienergy computed tomography
O. Semerci, N. Hao, M. E. Kilmer, and E. L. Miller · 2014
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Learning overcomplete latent variable models through tensor methods
A. Anandkumar, R. Ge, and M. Janzamin · 2015
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Convex optimization: Algorithms and complexity
S. Bubeck · 2015
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Phase retrieval via wirtinger flow: Theory and algorithms
E. J. Candes, X. Li, and M. Soltanolkotabi · 2015
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Y. Chen and M. J. Wainwright · 2015
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On the impact of predictor geometry on the performance on high-dimensional ridge-regularized generalized robust regression estimators
N. El Karoui · 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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Provable models for robust low-rank tensor completion
B. Huang, C. Mu, D. Goldfarb, and J. Wright · 2015
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Tensor sparsification via a bound on the spectral norm of random tensors
N. H. Nguyen, P. Drineas, and T. D. Tran · 2015
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Guaranteed tensor decomposition: A moment approach
G. Tang and P. Shah · 2015
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Parallel matrix factorization for low-rank tensor completion
Y. Xu, R. Hao, W. Yin, and Z. Su · 2015
Statistically optimal and computationally efficient low rank tensor completion from noisy entries
D. Xia, M. Yuan, and C.-H. Zhang · 2017
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Hankel matrix nuclear norm regularized tensor completion for n n -dimensional exponential signals
J. Ying, H. Lu, Q. Wei, J.-F. Cai, D. Guo, J. Wu, Z. Chen, and X. Qu · 2017
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Incoherent tensor norms and their applications in higher order tensor completion
M. Yuan and C.-H. Zhang · 2017
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Exact tensor completion using t-svd
Z. Zhang and S. Aeron · 2017
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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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Noisy tensor completion via the sum-of-squares hierarchy
B. Barak and A. Moitra · 2016
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An overview of low-rank matrix recovery from incomplete observations
M. A. Davenport and J. Romberg · 2016
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Fast spectral algorithms from sum-of-squares proofs: tensor decomposition and planted sparse vectors
S. B. Hopkins, T. Schramm, J. Shi, and D. Steurer · 2016
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Tensor completion using total variation and low-rank matrix factorization
T.-Y. Ji, T.-Z. Huang, X.-L. Zhao, T.-H. Ma, and G. Liu · 2016
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Low-rank tensor completion: a riemannian manifold preconditioning approach
H. Kasai and B. Mishra · 2016
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Tensor robust principal component analysis: Exact recovery of corrupted low-rank tensors via convex optimization
C. Lu, J. Feng, Y. Chen, W. Liu, Z. Lin, and S. Yan · 2016
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L. Ding and Y. Chen · 2018
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Efficient dictionary learning with gradient descent
D. Gilboa, S. Buchanan, and J. Wright · 2018
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Spectral algorithms for tensor completion
A. Montanari and N. Sun · 2018
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High-dimensional probability: An introduction with applications in data science
R. Vershynin · 2018
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Scalable tensor completion with nonconvex regularization
Q. Yao · 2018
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Near-optimal bounds for phase synchronization
Y. Zhong and N. Boumal · 2018
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Robust statistics for signal processing
A. M. Zoubir, V. Koivunen, E. Ollila, and M. Muma · 2018
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Tensor SVD: Statistical and computational limits
A. Zhang and D. Xia · 2018
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Y. Chen, Y. Chi, J. Fan, C. Ma, and Y. Yan · 2019
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Gradient descent with random initialization: Fast global convergence for nonconvex phase retrieval
Y. Chen, Y. Chi, J. Fan, and C. Ma · 2019
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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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Nonconvex optimization meets low-rank matrix factorization: An overview
Y. Chi, Y. Lu, and Y. Chen · 2019
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J. Chen, D. Liu, and X. Li · 2019
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Nonconvex low-rank tensor completion from noisy data
C. Cai, G. Li, H. V. Poor, and Y. Chen · 2019
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Non-convex projected gradient descent for generalized low-rank tensor regression
H. Chen, G. Raskutti, and M. Yuan · 2019
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Tensor robust principal component analysis: Better recovery with atomic norm regularization
D. Driggs, S. Becker, and J. Boyd-Graber · 2019
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Learning preferences with side information
V. F. Farias and A. A. Li · 2019
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Sparse tensor additive regression
B. Hao, B. Wang, P. Wang, J. Zhang, J. Yang, and W. W. Sun · 2019
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The non-convex geometry of low-rank matrix optimization
Q. Li, Z. Zhu, and G. Tang · 2019
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Machine learning for problems with missing and uncertain data with applications to personalized medicine
C. Pawlowski · 2019
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A. Pananjady and M. J. Wainwright · 2019
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Iterative collaborative filtering for sparse noisy tensor estimation
D. Shah and C. L. Yu · 2019
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Y. S. Tan and R. Vershynin · 2019
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Cross: Efficient low-rank tensor completion
A. Zhang · 2019
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Subspace estimation from unbalanced and incomplete data matrices: ℓ 2 , ∞ \ell_{2,\infty} statistical guarantees
C. Cai, G. Li, Y. Chi, H. V. Poor, and Y. Chen · 2020
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Sparse and low-rank tensor estimation via cubic sketchings
B. Hao, A. Zhang, and G. Cheng · 2020
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Data analytics in operations management: A review
V. V. Mišić and G. Perakis · 2020
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