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Noisy matrix completion aims at estimating a low-rank matrix given only partial and corrupted entries.
Matrix equation X A + B X = C {XA+BX=C}
RA Smith · 1968
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Perturbation bounds in connection with singular value decomposition
Per-Åke Wedin · 1972
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On the perturbation of pseudo-inverses, projections and linear least squares problems
Gilbert W Stewart · 1977
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Perturbation bounds for matrix square roots and Pythagorean sums
Bernhard A. Schmitt · 1992
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Matrix rank minimization with applications
Maryam Fazel · 2002
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Mathematical Statistics
J. Shao · 2003
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Learning with matrix factorizations
Nathan Srebro · 2004
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Fast maximum margin matrix factorization for collaborative prediction
Jasson DM Rennie and Nathan Srebro · 2005
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Rank, trace-norm and max-norm
Nathan Srebro and Adi Shraibman · 2005
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Confidence intervals for diffusion index forecasts and inference for factor-augmented regressions
Jushan Bai and Serena Ng · 2006
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Sparse principal component analysis
Hui Zou, Trevor Hastie, and Robert Tibshirani · 2006
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Theory of semidefinite programming for sensor network localization
Anthony Man-Cho So and Yinyu Ye · 2007
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Exact matrix completion via convex optimization
Emmanuel Candès and Benjamin Recht · 2009
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Guaranteed rank minimization via singular value projection
Raghu Meka, Prateek Jain, and Inderjit S. Dhillon · 2009
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P-values for high-dimensional regression
Nicolai Meinshausen, Lukas Meier, and Peter Bühlmann · 2009
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High dimensional variable selection
Larry Wasserman and Kathryn Roeder · 2009
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Matrix completion with noise
Emmanuel Candès and Yaniv Plan · 2010
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Guaranteed rank minimization via singular value projection
Prateek Jain, Raghu Meka, and Inderjit S Dhillon · 2010
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Matrix completion from a few entries
R. H. Keshavan, A. Montanari, and S. Oh · 2010
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Matrix completion from noisy entries
Raghunandan H. Keshavan, Andrea Montanari, and Sewoong Oh · 2010
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Spectral regularization algorithms for learning large incomplete matrices
R. Mazumder, T. Hastie, and R. Tibshirani · 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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Inference for high-dimensional sparse econometric models
Alexandre Belloni, Victor Chernozhukov, and Christian Hansen · 2011
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Robust principal component analysis?
Emmanuel Candès, Xiaodong Li, Yi Ma, and John Wright · 2011
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Rank-sparsity incoherence for matrix decomposition
Venkat Chandrasekaran, Sujay Sanghavi, Pablo A Parrilo, and Alan S Willsky · 2011
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Low-rank matrix recovery via iteratively reweighted least squares minimization
Massimo Fornasier, Holger Rauhut, and Rachel Ward · 2011
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Concentration-based guarantees for low-rank matrix reconstruction
Rina Foygel and Nathan Srebro · 2011
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Recovering low-rank matrices from few coefficients in any basis
David Gross · 2011
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Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion
Vladimir Koltchinskii, Karim Lounici, and Alexandre B. Tsybakov · 2011
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Oracle inequalities in empirical risk minimization and sparse recovery problems
Vladimir Koltchinskii · 2011
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Factor models and variable selection in high-dimensional regression analysis
Alois Kneip and Pascal Sarda · 2011
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A simpler approach to matrix completion
Benjamin Recht · 2011
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Estimation of high-dimensional low-rank matrices
Angelika Rohde and Alexandre B Tsybakov · 2011
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Angular synchronization by eigenvectors and semidefinite programming
Amit Singer · 2011
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A tail inequality for quadratic forms of subgaussian random vectors
Daniel Hsu, Sham M. Kakade, and Tong 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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Calibrated elastic regularization in matrix completion
Tingni Sun and Cun-Hui Zhang · 2012
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Solving a low-rank factorization model for matrix completion by a nonlinear successive over-relaxation algorithm
Zaiwen Wen, Wotao Yin, and Yin Zhang · 2012
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Sparse PCA: Optimal rates and adaptive estimation
T Tony Cai, Zongming Ma, and Yihong Wu · 2013
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A max-norm constrained minimization approach to 1-bit matrix completion
Tony Cai and Wen-Xin Zhou · 2013
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On robust regression with high-dimensional predictors
Noureddine El Karoui, Derek Bean, Peter J Bickel, Chinghway Lim, and Bin Yu · 2013
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Large covariance estimation by thresholding principal orthogonal complements
J. Fan, Y. Liao, and M. Mincheva · 2013
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Low-rank matrix completion using alternating minimization
P. Jain, P. Netrapalli, and S. Sanghavi · 2013
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Improved iteratively reweighted least squares for unconstrained smoothed ℓ q \ell_{q} minimization
M. Lai, Y. Xu, and W. Yin · 2013
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Low-rank matrix completion by riemannian optimization
Bart Vandereycken · 2013
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Robust spectral compressed sensing via structured matrix completion
Yuxin Chen and Yuejie Chi · 2014
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1-bit matrix completion
Mark A Davenport, Yaniv Plan, Ewout Van Den Berg, and Mary Wootters · 2014
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Understanding alternating minimization for matrix completion
Moritz Hardt · 2014
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Confidence intervals for high-dimensional linear regression: Minimax rates and adaptivity
T Tony Cai and Zijian Guo · 2017
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Ji Chen and Xiaodong Li · 2017
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High-dimensional simultaneous inference with the bootstrap
Ruben Dezeure, Peter Bühlmann, and Cun-Hui Zhang · 2017
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Solving (most) of a set of quadratic equalities: Composite optimization for robust phase retrieval
John C Duchi and Feng Ruan · 2017
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No spurious local minima in nonconvex low rank problems: A unified geometric analysis
Rong Ge, Chi Jin, and Yi Zheng · 2017
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Confidence intervals and hypothesis testing for high-dimensional regression
Adel Javanmard and Andrea Montanari · 2014
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Hypothesis testing in high-dimensional regression under the gaussian random design model: Asymptotic theory
Adel Javanmard and Andrea Montanari · 2014
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Noisy low-rank matrix completion with general sampling distribution
Olga Klopp · 2014
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A significance test for the lasso
Richard Lockhart, Jonathan Taylor, Ryan J Tibshirani, and Robert Tibshirani · 2014
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Proximal algorithms
Neal Parikh and Stephen Boyd · 2014
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On asymptotically optimal confidence regions and tests for high-dimensional models
Sara van de Geer, Peter Bühlmann, Ya’acov Ritov, and Ruben Dezeure · 2014
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Honest confidence regions and optimality in high-dimensional precision matrix estimation
Jana Janková and Sara van de Geer · 2017
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Inter-subject analysis: Inferring sparse interactions with dense intra-graphs
Cong Ma, Junwei Lu, and Han Liu · 2017
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Cong Ma, Kaizheng Wang, Yuejie Chi, and Yuxin Chen · 2017
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Active matrix completion with uncertainty quantification
Simon Mak and Yao Xie · 2017
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A general theory of hypothesis tests and confidence regions for sparse high dimensional models
Yang Ning and Han Liu · 2017
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High dimensional probability, 2017
Roman Vershynin · 2017
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Simultaneous inference for high-dimensional linear models
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Approximate residual balancing: debiased inference of average treatment effects in high dimensions
Susan Athey, Guido W Imbens, and Stefan Wager · 2018
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Distributed testing and estimation under sparse high dimensional models
Heather Battey, Jianqing Fan, Han Liu, Junwei Lu, and Ziwei Zhu · 2018
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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
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The projected power method: An efficient algorithm for joint alignment from pairwise differences
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Double/debiased machine learning for treatment and structural parameters, 2018
Victor Chernozhukov, Denis Chetverikov, Mert Demirer, Esther Duflo, Christian Hansen, Whitney Newey, and James Robins · 2018
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Asymmetry helps: Eigenvalue and eigenvector analyses of asymmetrically perturbed low-rank matrices
Yuxin Chen, Chen Cheng, and Jianqing Fan · 2018
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Adaptive confidence sets for matrix completion
Alexandra Carpentier, Olga Klopp, Matthias Löffler, and Richard Nickl · 2018
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The leave-one-out approach for matrix completion: Primal and dual analysis
Lijun Ding and Yudong Chen · 2018
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Principal component analysis for big data
Jianqing Fan, Qiang Sun, Wen-Xin Zhou, and Ziwei Zhu · 2018
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De-biased sparse pca: Inference and testing for eigenstructure of large covariance matrices
Jana Janková and Sara van de Geer · 2018
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A unified theory of confidence regions and testing for high-dimensional estimating equations
Matey Neykov, Yang Ning, Jun S Liu, and Han Liu · 2018
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Confidence interval of singular vectors for high-dimensional and low-rank matrix regression
Dong Xia · 2018
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How much restricted isometry is needed in nonconvex matrix recovery?
Richard Zhang, Cédric Josz, Somayeh Sojoudi, and Javad Lavaei · 2018
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A primal-dual analysis of global optimality in nonconvex low-rank matrix recovery
Xiao Zhang, Lingxiao Wang, Yaodong Yu, and Quanquan Gu · 2018
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Low-rank matrix recovery with composite optimization: good conditioning and rapid convergence
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