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Tensors, which provide a powerful and flexible model for representing multi-attribute data and multi-way interactions, play an indispensable role in modern data science across various fields in science and engineering.
Some mathematical notes on three-mode factor analysis
L. R. Tucker · 1966
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A multilinear singular value decomposition
L. De Lathauwer, B. De Moor, and J. Vandewalle · 2000
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On the best rank-1 and rank- ( R 1 , R 2 , … , R N ) (R_{1},R_{2},\dots,R_{N}) approximation of higher-order tensors
L. De Lathauwer, B. De Moor, and J. Vandewalle · 2000
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Adaptive estimation of a quadratic functional by model selection
B. Laurent and P. Massart · 2000
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Construction and analysis of degenerate PARAFAC models
P. Paatero · 2000
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Tensor decompositions and applications
T. G. Kolda and B. W. Bader · 2009
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The power of convex relaxation: Near-optimal matrix completion
E. J. Candès and T. Tao · 2010
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Multiverse recommendation: n n -dimensional tensor factorization for context-aware collaborative filtering
A. Karatzoglou, X. Amatriain, L. Baltrunas, and N. Oliver · 2010
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Temporal collaborative filtering with bayesian probabilistic tensor factorization
L. Xiong, X. Chen, T.-K. Huang, J. Schneider, and J. G. Carbonell · 2010
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Tensor completion and low-n-rank tensor recovery via convex optimization
S. Gandy, B. Recht, and I. Yamada · 2011
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Tensor spaces and numerical tensor calculus
W. Hackbusch · 2012
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Tensor completion for estimating missing values in visual data
J. Liu, P. Musialski, P. Wonka, and J. Ye · 2012
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Most tensor problems are NP-hard
C. J. Hillar and L.-H. Lim · 2013
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Low-rank matrix and tensor completion via adaptive sampling
A. Krishnamurthy and A. Singh · 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 regression with applications in neuroimaging data analysis
H. Zhou, L. Li, and H. Zhu · 2013
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Tensor decompositions for learning latent variable models
A. Anandkumar, R. Ge, D. Hsu, S. Kakade, and M. Telgarsky · 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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Low-rank tensor completion by Riemannian optimization
D. Kressner, M. Steinlechner, and B. Vandereycken · 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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Novel methods for multilinear data completion and de-noising based on tensor-SVD
Z. Zhang, G. Ely, S. Aeron, N. Hao, and M. Kilmer · 2014
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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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Provable models for robust low-rank tensor completion
B. Huang, C. Mu, D. Goldfarb, and J. Wright · 2015
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Overcomplete tensor decomposition via convex optimization
Q. Li, A. Prater, L. Shen, and G. Tang · 2015
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Noisy tensor completion via the sum-of-squares hierarchy
B. Barak and A. Moitra · 2016
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Low-rank tensor completion: a Riemannian manifold preconditioning approach
H. Kasai and B. Mishra · 2016
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Tensors for data mining and data fusion: Models, applications, and scalable algorithms
E. E. Papalexakis, C. Faloutsos, and N. D. Sidiropoulos · 2016
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Guaranteed matrix completion via non-convex factorization
R. Sun and Z.-Q. Luo · 2016
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On tensor completion via nuclear norm minimization
M. Yuan and C.-H. Zhang · 2016
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Exact tensor completion using t-SVD
Z. Zhang and S. Aeron · 2016
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Provable non-convex phase retrieval with outliers: Median truncated Wirtinger flow
H. Zhang, Y. Chi, and Y. Liang · 2016
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Solving random quadratic systems of equations is nearly as easy as solving linear systems
Y. Chen and E. Candès · 2017
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Hyperspectral image super-resolution via non-local sparse tensor factorization
R. Dian, L. Fang, and S. Li · 2017
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Tensor and its Tucker core: the invariance relationships
B. Jiang, F. Yang, and S. Zhang · 2017
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Non-square matrix sensing without spurious local minima via the Burer-Monteiro approach
D. Park, A. Kyrillidis, C. Carmanis, and S. Sanghavi · 2017
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Exact tensor completion with sum-of-squares
A. Potechin and D. Steurer · 2017
On polynomial time methods for exact low-rank tensor completion
D. Xia and M. Yuan · 2019
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Cross: Efficient low-rank tensor completion
A. Zhang · 2019
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Tensor regression using low-rank and sparse Tucker decompositions
T. Ahmed, H. Raja, and W. U. Bajwa · 2020
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Deep networks and the multiple manifold problem
S. Buchanan, D. Gilboa, and J. Wright · 2020
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On the non-asymptotic concentration of heteroskedastic Wishart-type matrix
T. T. Cai, R. Han, and A. R. Zhang · 2020
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Nonconvex rectangular matrix completion via gradient descent without ℓ 2 , ∞ \ell_{2,\infty} regularization
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Low rank tensor recovery via iterative hard thresholding
H. Rauhut, R. Schneider, and Ž. Stojanac · 2017
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Tensor decomposition for signal processing and machine learning
N. D. Sidiropoulos, L. De Lathauwer, X. Fu, K. Huang, E. E. Papalexakis, and C. Faloutsos · 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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Complete dictionary recovery over the sphere ii: Recovery by Riemannian trust-region method
J. Sun, Q. Qu, and J. Wright · 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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Subgradient descent learns orthogonal dictionaries
Y. Bai, Q. Jiang, and J. Sun · 2018
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J. Chen, D. Liu, and X. Li · 2020
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Uncertainty quantification for nonconvex tensor completion: Confidence intervals, heteroscedasticity and optimality
C. Cai, H. V. Poor, and Y. Chen · 2020
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Guaranteed recovery of one-hidden-layer neural networks via cross entropy
H. Fu, Y. Chi, and Y. Liang · 2020
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Optimization landscape of Tucker decomposition
A. Frandsen and R. Ge · 2020
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On the optimization landscape of tensor decompositions
R. Ge and T. Ma · 2020
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An optimal statistical and computational framework for generalized tensor estimation
R. Han, R. Willett, and A. Zhang · 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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Non-convex low-rank matrix recovery with arbitrary outliers via median-truncated gradient descent
Y. Li, Y. Chi, H. Zhang, and Y. Liang · 2020
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Tensor completion made practical
A. Liu and A. Moitra · 2020
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Inference for low-rank tensors–no need to debias
D. Xia, A. R. Zhang, and Y. Zhou · 2020
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ISLET: Fast and optimal low-rank tensor regression via importance sketching
A. Zhang, Y. Luo, G. Raskutti, and M. Yuan · 2020
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From symmetry to geometry: Tractable nonconvex problems
Y. Zhang, Q. Qu, and J. Wright · 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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Spectral methods for data science: A statistical perspective
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Generalized low-rank plus sparse tensor estimation by fast Riemannian optimization
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Manifold gradient descent solves multi-channel sparse blind deconvolution provably and efficiently
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Statistical inferences of linear forms for noisy matrix completion
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