Fetching the paper…
Reading the bibliography…
In this work, we study the performance of sub-gradient method (SubGM) on a natural nonconvex and nonsmooth formulation of low-rank matrix recovery with $\ell_1$-loss, where the goal is to recover a low-rank matrix from a limited number of measurements, a subset of which may be grossly corrupted with noise.
Optimization and nonsmooth analysis
Frank H Clarke · 1990
Earlier work this paper cites.
Relative perturbation techniques for singular value problems
Stanley C Eisenstat and Ilse CF Ipsen · 1995
Earlier work this paper cites.
Sparse approximate solutions to linear systems
Balas Kausik Natarajan · 1995
Earlier work this paper cites.
Relative perturbation results for eigenvalues and eigenvectors of diagonalisable matrices
Stanley C Eisenstat and Ilse CF Ipsen · 1998
Earlier work this paper cites.
A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization
Samuel Burer and Renato DC Monteiro · 2003
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.
Tight oracle inequalities for low-rank matrix recovery from a minimal number of noisy random measurements
Emmanuel J Candes and Yaniv Plan · 2011
Earlier work this paper cites.
Zhiyuan Li, Yuping Luo, and Kaifeng Lyu · 2012
Earlier work this paper cites.
Robust pca via principal component pursuit: A review for a comparative evaluation in video surveillance
Thierry Bouwmans and El Hadi Zahzah · 2014
Earlier work this paper cites.
Extracting sparse error of robust pca for face recognition in the presence of varying illumination and occlusion
Xiao Luan, Bin Fang, Linghui Liu, Weibin Yang, and Jiye Qian · 2014
Earlier work this paper cites.
An efficient non-negative matrix-factorization-based approach to collaborative filtering for recommender systems
Xin Luo, Mengchu Zhou, Yunni Xia, and Qingsheng Zhu · 2014
Earlier work this paper cites.
Probability in high dimension
Ramon Van Handel · 2014
Earlier work this paper cites.
Yudong Chen and Martin J Wainwright · 2015
Earlier work this paper cites.
Qinqing Zheng and John Lafferty · 2015
Cited alongside, same era.
Global optimality of local search for low rank matrix recovery
Srinadh Bhojanapalli, Behnam Neyshabur, and Nathan Srebro · 2016
Cited alongside, same era.
On perturbation bounds for orthogonal projections
Yan Mei Chen, Xiao Shan Chen, and Wen Li · 2016
Cited alongside, same era.
Matrix completion has no spurious local minimum
Rong Ge, Jason D Lee, and Tengyu Ma · 2016
Cited alongside, same era.
Deep learning without poor local minima
Kenji Kawaguchi · 2016
Nonconvex matrix factorization from rank-one measurements
Yuanxin Li, Cong Ma, Yuxin Chen, and Yuejie Chi · 2019
Later among the works it cites.
Analysis of the optimization landscapes for overcomplete representation learning
Qing Qu, Yuexiang Zhai, Xiao Li, Yuqian Zhang, and Zhihui Zhu · 2019
Later among the works it cites.
High-dimensional statistics: A non-asymptotic viewpoint , volume 48
Martin J Wainwright · 2019
Later among the works it cites.
Sharp restricted isometry bounds for the inexistence of spurious local minima in nonconvex matrix recovery
Richard Y Zhang, Somayeh Sojoudi, and Javad Lavaei · 2019
Later among the works it cites.
Exact guarantees on the absence of spurious local minima for non-negative rank-1 robust principal component analysis
Salar Fattahi and Somayeh Sojoudi · 2020
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
Complete dictionary recovery over the sphere i: Overview and the geometric picture
Ju Sun, Qing Qu, and John Wright · 2016
Cited alongside, same era.
Low-rank solutions of linear matrix equations via procrustes flow
Stephen Tu, Ross Boczar, Max Simchowitz, Mahdi Soltanolkotabi, and Ben Recht · 2016
Cited alongside, same era.
No spurious local minima in nonconvex low rank problems: A unified geometric analysis
Rong Ge, Chi Jin, and Yi Zheng · 2017
Cited alongside, same era.
Implicit regularization in matrix factorization
Suriya Gunasekar, Blake Woodworth, Srinadh Bhojanapalli, Behnam Neyshabur, and Nathan Srebro · 2018
Cited alongside, same era.
A theory on the absence of spurious solutions for nonconvex and nonsmooth optimization
Cedric Josz, Yi Ouyang, Richard Y Zhang, Javad Lavaei, and Somayeh Sojoudi · 2018
Cited alongside, same era.
Algorithmic regularization in over-parameterized matrix sensing and neural networks with quadratic activations
Yuanzhi Li, Tengyu Ma, and Hongyang Zhang · 2018
Cited alongside, same era.
Nonconvex optimization meets low-rank matrix factorization: An overview
Yuejie Chi, Yue M Lu, and Yuxin Chen · 2019
Cited alongside, same era.
Yuqian Zhang, Qing Qu, and John Wright · 2020
Later among the works it cites.
Gradient descent on neural networks typically occurs at the edge of stability
Jeremy M Cohen, Simran Kaur, Yuanzhi Li, J Zico Kolter, and Ameet Talwalkar · 2021
Later among the works it cites.
Rank overspecified robust matrix recovery: Subgradient method and exact recovery
Lijun Ding, Liwei Jiang, Yudong Chen, Qing Qu, and Zhihui Zhu · 2021
Later among the works it cites.
Dominik Stöger and Mahdi Soltanolkotabi · 2021
Later among the works it cites.
Accelerating ill-conditioned low-rank matrix estimation via scaled gradient descent
Tian Tong, Cong Ma, and Yuejie Chi · 2021
Later among the works it cites.
Preconditioned gradient descent for over-parameterized nonconvex matrix factorization
Jialun Zhang, Salar Fattahi, and Richard Zhang · 2021
Later among the works it cites.
Sharp global guarantees for nonconvex low-rank matrix recovery in the overparameterized regime
Richard Y Zhang · 2021
Later among the works it cites.
On the computational and statistical complexity of over-parameterized matrix sensing
Jiacheng Zhuo, Jeongyeol Kwon, Nhat Ho, and Constantine Caramanis · 2021
Later among the works it cites.