Fetching the paper…
Reading the bibliography…
Many problems encountered in science and engineering can be formulated as estimating a low-rank object (e.g., matrices and tensors) from incomplete, and possibly corrupted, linear measurements.
Some mathematical notes on three-mode factor analysis
Ledyard R Tucker · 1966
Earlier work this paper cites.
Neural networks and principal component analysis: Learning from examples without local minima
Pierre Baldi and Kurt Hornik · 1989
Earlier work this paper cites.
Cubic regularization of Newton method and its global performance
Yurii Nesterov and Boris T Polyak · 2006
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.
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. Candès, Xiaodong Li, Yi Ma, and John Wright · 2011
Earlier work this paper cites.
Tight oracle inequalities for low-rank matrix recovery from a minimal number of noisy random measurements
Emmanuel J Candès and Yaniv Plan · 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.
Low-rank matrix completion using alternating minimization
Prateek Jain, Praneeth Netrapalli, and Sujay Sanghavi · 2013
Earlier work this paper cites.
Fast matrix completion without the condition number
Moritz Hardt and Mary Wootters · 2014
Earlier work this paper cites.
Non-convex robust PCA
Praneeth Netrapalli, UN Niranjan, Sujay Sanghavi, Animashree Anandkumar, and Prateek Jain · 2014
Earlier work this paper cites.
Phase retrieval via Wirtinger flow: Theory and algorithms
Emmanuel Candès, Xiaodong Li, and Mahdi Soltanolkotabi · 2015
Earlier work this paper cites.
Incoherence-optimal matrix completion
Yudong Chen · 2015
Earlier work this paper cites.
Yudong Chen and Martin J Wainwright · 2015
Earlier work this paper cites.
Escaping from saddle points-online stochastic gradient for tensor decomposition
Rong Ge, Furong Huang, Chi Jin, and Yang Yuan · 2015
Earlier work this paper cites.
Provable models for robust low-rank tensor completion
Bo Huang, Cun Mu, Donald Goldfarb, and John Wright · 2015
Earlier work this paper cites.
Complete dictionary recovery using nonconvex optimization
Ju Sun, Qing Qu, and John Wright · 2015
Earlier work this paper cites.
A convergent gradient descent algorithm for rank minimization and semidefinite programming from random linear measurements
Qinqing Zheng and John Lafferty · 2015
Earlier work this paper cites.
Noisy tensor completion via the sum-of-squares hierarchy
Boaz Barak and Ankur Moitra · 2016
Earlier work this paper cites.
Global optimality of local search for low rank matrix recovery
Srinadh Bhojanapalli, Behnam Neyshabur, and Nati Srebro · 2016
Earlier work this paper cites.
Matrix completion has no spurious local minimum
Rong Ge, Jason D Lee, and Tengyu Ma · 2016
Earlier work this paper cites.
Low-rank tensor completion: a Riemannian manifold preconditioning approach
Hiroyuki Kasai and Bamdev Mishra · 2016
Earlier work this paper cites.
Deep learning without poor local minima
Kenji Kawaguchi · 2016
Earlier work this paper cites.
Guaranteed matrix completion via non-convex factorization
Ruoyu Sun and Zhi-Quan Luo · 2016
Cited alongside, same era.
Low-rank solutions of linear matrix equations via Procrustes flow
Stephen Tu, Ross Boczar, Max Simchowitz, Mahdi Soltanolkotabi, and Benjamin Recht · 2016
Cited alongside, same era.
Guarantees of Riemannian optimization for low rank matrix recovery
Ke Wei, Jian-Feng Cai, Tony F Chan, and Shingyu Leung · 2016
Cited alongside, same era.
Fast algorithms for robust PCA via gradient descent
Xinyang Yi, Dohyung Park, Yudong Chen, and Constantine Caramanis · 2016
Cited alongside, same era.
On tensor completion via nuclear norm minimization
Ming Yuan and Cun-Hui Zhang · 2016
Cited alongside, same era.
Convex regularization for high-dimensional multiresponse tensor regression
Garvesh Raskutti, Ming Yuan, and Han Chen · 2019
Later among the works it cites.
On polynomial time methods for exact low-rank tensor completion
Dong Xia and Ming Yuan · 2019
Later among the works it cites.
Nonconvex rectangular matrix completion via gradient descent without ℓ 2 , ∞ \ell_{2,\infty} regularization
Ji Chen, Dekai Liu, and Xiaodong Li · 2020
Later among the works it cites.
Noisy matrix completion: Understanding statistical guarantees for convex relaxation via nonconvex optimization
Yuxin Chen, Yuejie Chi, Jianqing Fan, Cong Ma, and Yuling Yan · 2020
Later among the works it cites.
The nonsmooth landscape of phase retrieval
Damek Davis, Dmitriy Drusvyatskiy, and Courtney Paquette · 2020
Later among the works it cites.
Optimization landscape of Tucker decomposition
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Qinqing Zheng and John Lafferty · 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.
Non-convex optimization for machine learning
Prateek Jain and Purushottam Kar · 2017
Cited alongside, same era.
How to escape saddle points efficiently
Chi Jin, Rong Ge, Praneeth Netrapalli, Sham M Kakade, and Michael I Jordan · 2017
Cited alongside, same era.
Non-square matrix sensing without spurious local minima via the Burer-Monteiro approach
Dohyung Park, Anastasios Kyrillidis, Constantine Carmanis, and Sujay Sanghavi · 2017
Cited alongside, same era.
Low rank tensor recovery via iterative hard thresholding
Holger Rauhut, Reinhold Schneider, and Željka Stojanac · 2017
Cited alongside, same era.
Optimization methods for large-scale machine learning
Léon Bottou, Frank E Curtis, and Jorge Nocedal · 2018
Cited alongside, same era.
Abraham Frandsen and Rong Ge · 2020
Later among the works it cites.
Inference for low-rank tensors–no need to debias
Dong Xia, Anru R Zhang, and Yuchen Zhou · 2020
Later among the works it cites.
Subspace estimation from unbalanced and incomplete data matrices: ℓ 2 , ∞ \ell_{2,\infty} statistical guarantees
Changxiao Cai, Gen Li, Yuejie Chi, H Vincent Poor, and Yuxin Chen · 2021
Later among the works it cites.
Generalized low-rank plus sparse tensor estimation by fast Riemannian optimization
Jian-Feng Cai, Jingyang Li, and Dong Xia · 2021
Later among the works it cites.
Low-rank matrix recovery with composite optimization: good conditioning and rapid convergence
Vasileios Charisopoulos, Yudong Chen, Damek Davis, Mateo Díaz, Lijun Ding, and Dmitriy Drusvyatskiy · 2021
Later among the works it cites.
Bridging convex and nonconvex optimization in robust PCA: Noise, outliers, and missing data
Yuxin Chen, Jianqing Fan, Cong Ma, and Yuling Yan · 2021
Later among the works it cites.
Nonconvex matrix factorization from rank-one measurements
Yuanxin Li, Cong Ma, Yuxin Chen, and Yuejie Chi · 2021
Later among the works it cites.
Yuetian Luo and Anru R Zhang · 2021
Later among the works it cites.
Beyond Procrustes: Balancing-free gradient descent for asymmetric low-rank matrix sensing
Cong Ma, Yuanxin Li, and Yuejie Chi · 2021
Later among the works it cites.
Manifold gradient descent solves multi-channel sparse blind deconvolution provably and efficiently
Laixi Shi and Yuejie Chi · 2021
Later among the works it cites.
Small random initialization is akin to spectral learning: Optimization and generalization guarantees for overparameterized low-rank matrix reconstruction
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.
Haifeng Wang, Jinchi Chen, and Ke Wei · 2021
Later among the works it cites.
Statistically optimal and computationally efficient low rank tensor completion from noisy entries
Dong Xia, Ming Yuan, and Cun-Hui Zhang · 2021
Later among the works it cites.
An optimal statistical and computational framework for generalized tensor estimation
Rungang Han, Rebecca Willett, and Anru R Zhang · 2022
Later among the works it cites.
Scaling and scalability: Provable nonconvex low-rank tensor estimation from incomplete measurements
Tian Tong, Cong Ma, Ashley Prater-Bennette, Erin Tripp, and Yuejie Chi · 2022
Later among the works it cites.
Fast and provable tensor robust principal component analysis via scaled gradient descent
Harry Dong, Tian Tong, Cong Ma, and Yuejie Chi · 2023
Closest in time.
The power of preconditioning in overparameterized low-rank matrix sensing
Xingyu Xu, Yandi Shen, Yuejie Chi, and Cong Ma · 2023
Closest in time.