Fetching the paper…
Reading the bibliography…
Optimization problems with rank constraints arise in many applications, including matrix regression, structured PCA, matrix completion and matrix decomposition problems.
“Interior Point Polynomial Algorithms in Convex Programming”, SIAM studies in applied and numerical mathematics
Y. Nesterov and A. Nemirovskii · 1987
Earlier work this paper cites.
“Probability in Banach Spaces: Isoperimetry and Processes”
M. Ledoux and M. Talagrand · 1991
Earlier work this paper cites.
“Nonlinear programming”
D.P. Bertsekas · 1995
Earlier work this paper cites.
“Matrix computations”
Gene˜H. Golub and Charles˜F. Van˜Loan · 1996
Earlier work this paper cites.
“Finding a large hidden clique in a random graph”
Noga Alon, Michael Krivelevich and Benny Sudakov · 1998
Earlier work this paper cites.
“Matrix Completion Problems”
M. Laurent · 2001
Earlier work this paper cites.
“The Concentration of Measure Phenomenon”, Mathematical Surveys and Monographs
M. Ledoux · 2001
Earlier work this paper cites.
“An O ( n ) O(n) algorithm for projecting a vector on the intersection of a hyperplane and a box in R n R^{n} ”
N. Maculan, C.˜P. Santiago, E.˜M. Macambira and M.˜H.˜C. Jardim · 2003
Earlier work this paper cites.
“Convex optimization”
S. Boyd and L. Vandenberghe · 2004
Earlier work this paper cites.
“Local minima and convergence in low-rank semidefinite programming”
Samuel Burer and Renato D.˜C. Monteiro · 2005
Earlier work this paper cites.
“Spectral techniques applied to sparse random graphs”
Uriel Feige and Eran Ofek · 2005
Earlier work this paper cites.
“Efficient projections onto the l 1-ball for learning in high dimensions”
John Duchi, Shai Shalev-Shwartz, Yoram Singer and Tushar Chandra · 2008
Earlier work this paper cites.
“High-dimensional analysis of semdefinite relaxations for sparse principal component analysis”
A.˜A. Amini and M.˜J. Wainwright · 2009
Earlier work this paper cites.
“Exact matrix completion via convex optimization”
Emmanuel˜J. Cand\‘es and Benjamin Recht · 2009
Earlier work this paper cites.
“On consistency and sparsity for principal components analysis in high dimensions”
I.˜M. Johnstone and A.˜Y. Lu · 2009
Earlier work this paper cites.
“Estimation of (near) low-rank matrices with noise and high-dimensional scaling”
Sahand Negahban and Martin˜J. Wainwright · 2009
Earlier work this paper cites.
“Guaranteed rank minimization via singular value projection”
Prateek Jain, Raghu Meka and Inderjit˜S. Dhillon · 2010
Earlier work this paper cites.
“Matrix completion from a few entries”
Raghunandan˜H. Keshavan, Andrea Montanari and Sewoong Oh · 2010
Earlier work this paper cites.
“Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization”
Benjamin Recht, Maryam Fazel and Pablo˜A. Parrilo · 2010
Earlier work this paper cites.
“Robust principal component analysis?”
Emmanuel˜J. Cand\‘es, Xiaodong Li, Yi Ma and John Wright · 2011
Earlier work this paper cites.
“Rank-Sparsity Incoherence for Matrix Decomposition”
Venkat Chandrasekaran, Sujay Sanghavi, Pablo Parrilo and Alan Willsky · 2011
Earlier work this paper cites.
“Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions”
Nathan Halko, Per-Gunnar Martinsson and Joel˜A. Tropp · 2011
Earlier work this paper cites.
“Robust matrix decomposition with sparse corruptions”
Daniel Hsu, Sham˜M. Kakade and Tong Zhang · 2011
Cited alongside, same era.
“Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion”
Vladimir Koltchinskii, Karim Lounici and Alexandre˜B. Tsybakov · 2011
Cited alongside, same era.
“Noisy matrix decomposition via convex relaxation: Optimal rates in high dimensions”
Alekh Agarwal, Sahand Negahban and Martin˜J. Wainwright · 2012
Cited alongside, same era.
“Minimax bounds for sparse PCA with noisy high-dimensional data”
A. Birnbaum, I.˜M. Johnstone, B. Nadler and D. Paul · 2012
Cited alongside, same era.
“High-dimensional regression with noisy and missing data: Provable guarantees with nonconvexity”
Po-Ling. Loh and Martin˜J. Wainwright · 2012
Cited alongside, same era.
“Restricted strong convexity and weighted matrix completion: Optimal bounds with noise”
“1-bit matrix completion”
Mark˜A. Davenport, Yaniv Plan, Ewout Berg and Mary Wootters · 2014
Later among the works it cites.
“Global Convergence of Stochastic Gradient Descent for Some Nonconvex Matrix Problems”
Christopher De˜Sa, Kunle Olukotun and Christopher R\’e · 2014
Later among the works it cites.
“Minimax Estimation in Sparse Canonical Correlation Analysis”
Chao Gao, Zongming Ma, Zhao Ren and Harrison˜H. Zhou · 2014
Later among the works it cites.
“Understanding alternating minimization for matrix completion”
Moritz Hardt · 2014
Later among the works it cites.
“The Noisy Power Method: A Meta Algorithm with Applications”
Moritz Hardt and Eric Price · 2014
Later among the works it cites.
“Fast Matrix Completion Without the Condition Number”
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Sahand Negahban and Martin˜J. Wainwright · 2012
Cited alongside, same era.
“Efficient euclidean projections onto the intersection of norm balls”
Hao Su, Adams˜Wei Yu and Li Fei-Fei · 2012
Cited alongside, same era.
“Complexity theoretic lower bounds for sparse principal component detection”
Quentin Berthet and Philippe Rigollet · 2013
Cited alongside, same era.
“Sparse PCA: Optimal rates and adaptive estimation”
T˜Tony Cai, Zongming Ma and Yihong Wu · 2013
Cited alongside, same era.
“Optimal estimation and rank detection for sparse spiked covariance matrices”
Tony Cai, Zongming Ma and Yihong Wu · 2013
Cited alongside, same era.
“A max-norm constrained minimization approach to 1-bit matrix completion”
Tony Cai and Wen-Xin Zhou · 2013
Cited alongside, same era.
“Low-rank Matrix Recovery from Errors and Erasures”
Yudong Chen, Ali Jalali, Sujay Sanghavi and Constantine Caramanis · 2013
Cited alongside, same era.
Moritz Hardt and Mary Wootters · 2014
Later among the works it cites.
“On iterative hard thresholding methods for high-dimensional M-estimation”
Prateek Jain, Ambuj Tewari and Purushottam Kar · 2014
Later among the works it cites.
“Non-convex robust PCA”
Praneeth Netrapalli et al · 2014
Later among the works it cites.
“Algorithms and Theory for Clustering and Nonconvex Quadratic Programming”, 2014
Mahdi Soltanolkotabi · 2014
Later among the works it cites.
“Guaranteed Matrix Completion via Non-convex Factorization”
Ruoyu Sun and Zhi-Quan Luo · 2014
Later among the works it cites.
“Nonconvex statistical optimization: Minimax-optimal Sparse PCA in polynomial time”
Zhaoran Wang, Huanran Lu and Han Liu · 2014
Later among the works it cites.
Zhaoran Wang, Quanquan Gu, Yang Ning and Han Liu · 2014
Later among the works it cites.
“1-bit matrix completion under exact low-rank constraint”
Sonia˜A. Bhaskar and Adel Javanmard · 2015
Closest in time.
“Robust Regression via Hard Thresholding”
Kush Bhatia, Prateek Jain and Purushottam Kar · 2015
Closest in time.
Jian-Feng Cai, Suhui Liu and Weiyu Xu · 2015
Closest in time.
“Solving Random Quadratic Systems of Equations Is Nearly as Easy as Solving Linear Systems”
Yuxin Chen and Emmanuel˜J. Candes · 2015
Closest in time.
“Taming the Wild: A Unified Analysis of Hogwild!-Style Algorithms”
Christopher De˜Sa, Ce Zhang, Kunle Olukotun and Christopher R\’e · 2015
Closest in time.
“Low-rank Solutions of Linear Matrix Equations via Procrustes Flow”
Stephen Tu, Ross Boczar, Mahdi Soltanolkotabi and Benjamin Recht · 2015
Closest in time.
“The Local Convexity of Solving Quadratic Equations”
Chris˜D. White, Rachel Ward and Sujay Sanghavi · 2015
Closest in time.
“Global Convergence of a Grassmannian Gradient Descent Algorithm for Subspace Estimation”
Dejiao Zhang and Laura Balzano · 2015
Closest in time.
Qinqing Zheng and John Lafferty · 2015
Closest in time.
“Matrix completion from noisy entries”
Raghunandan˜H. Keshavan, Andrea Montanari and Sewoong Oh · 2078
Closest in time.