No Spurious Local Minima in Nonconvex Low Rank Problems: A Unified Geometric Analysis

3 April 2017

Papers citing "No Spurious Local Minima in Nonconvex Low Rank Problems: A Unified Geometric Analysis"

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Title
Provable Bregman-divergence based Methods for Nonconvex and Non-Lipschitz Problems Qiuwei Li Zhihui Zhu Gongguo Tang M. Wakin 9 26 0 22 Apr 2019
Proximal algorithms for constrained composite optimization, with applications to solving low-rank SDPs Yu Bai John C. Duchi Song Mei 14 5 0 01 Mar 2019
Noisy Matrix Completion: Understanding Statistical Guarantees for Convex Relaxation via Nonconvex Optimization Yuxin Chen Yuejie Chi Jianqing Fan Cong Ma Yuling Yan 20 128 0 20 Feb 2019
On Nonconvex Optimization for Machine Learning: Gradients, Stochasticity, and Saddle Points Chi Jin Praneeth Netrapalli Rong Ge Sham Kakade Michael I. Jordan 27 61 0 13 Feb 2019
What is Local Optimality in Nonconvex-Nonconcave Minimax Optimization? Chi Jin Praneeth Netrapalli Michael I. Jordan 21 82 0 02 Feb 2019
Passed & Spurious: Descent Algorithms and Local Minima in Spiked Matrix-Tensor Models Stefano Sarao Mannelli Florent Krzakala Pierfrancesco Urbani Lenka Zdeborová 16 48 0 01 Feb 2019
A Deterministic Gradient-Based Approach to Avoid Saddle Points L. Kreusser Stanley J. Osher Bao Wang ODL 32 3 0 21 Jan 2019
$Nonconvex Rectangular Matrix Completion via Gradient Descent without $\ell_{2,\infty}$ Regularization$ Nonconvex Rectangular Matrix Completion via Gradient Descent without $\ell_{2,\infty}$ Regularization Ji Chen Dekai Liu Xiaodong Li 13 11 0 18 Jan 2019
On the Global Convergence of Imitation Learning: A Case for Linear Quadratic Regulator Qi Cai Mingyi Hong Yongxin Chen Zhaoran Wang 27 34 0 11 Jan 2019
Sharp Restricted Isometry Bounds for the Inexistence of Spurious Local Minima in Nonconvex Matrix Recovery Richard Y. Zhang Somayeh Sojoudi Javad Lavaei 11 51 0 07 Jan 2019
Exact Guarantees on the Absence of Spurious Local Minima for Non-negative Rank-1 Robust Principal Component Analysis S. Fattahi Somayeh Sojoudi 19 38 0 30 Dec 2018
Bilinear Parameterization For Differentiable Rank-Regularization Marcus Valtonen Örnhag Carl Olsson A. Heyden 13 10 0 27 Nov 2018
Blind Over-the-Air Computation and Data Fusion via Provable Wirtinger Flow Jialin Dong Yuanming Shi Z. Ding 17 59 0 12 Nov 2018
Global Optimality in Distributed Low-rank Matrix Factorization Zhihui Zhu Qiuwei Li Xinshuo Yang Gongguo Tang Michael B. Wakin 14 4 0 07 Nov 2018
A biconvex optimization for solving semidefinite programs via bilinear factorization En-Liang Hu 11 0 0 03 Nov 2018
Recovery Guarantees for Quadratic Tensors with Sparse Observations Hongyang R. Zhang Vatsal Sharan Moses Charikar Yingyu Liang 21 2 0 31 Oct 2018
Subgradient Descent Learns Orthogonal Dictionaries Yu Bai Qijia Jiang Ju Sun 20 51 0 25 Oct 2018
Learning Two-layer Neural Networks with Symmetric Inputs Rong Ge Rohith Kuditipudi Zhize Li Xiang Wang OOD MLT 36 57 0 16 Oct 2018
Provable Subspace Tracking from Missing Data and Matrix Completion Praneeth Narayanamurthy Vahid Daneshpajooh Namrata Vaswani 19 22 0 06 Oct 2018
Stochastic Second-order Methods for Non-convex Optimization with Inexact Hessian and Gradient Liu Liu Xuanqing Liu Cho-Jui Hsieh Dacheng Tao ODL 11 10 0 26 Sep 2018
Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overview Yuejie Chi Yue M. Lu Yuxin Chen 39 416 0 25 Sep 2018
Nonconvex Demixing From Bilinear Measurements Jialin Dong Yuanming Shi 14 2 0 18 Sep 2018
$Streaming Kernel PCA with $\tilde{O}(\sqrt{n})$ Random Features$ Streaming Kernel PCA with $\tilde{O}(\sqrt{n})$ Random Features Enayat Ullah Poorya Mianjy T. V. Marinov R. Arora 33 20 0 02 Aug 2018
Optimistic mirror descent in saddle-point problems: Going the extra (gradient) mile P. Mertikopoulos Bruno Lecouat Houssam Zenati Chuan-Sheng Foo V. Chandrasekhar Georgios Piliouras 43 292 0 07 Jul 2018
On the Implicit Bias of Dropout Poorya Mianjy R. Arora René Vidal 27 66 0 26 Jun 2018
Defending Against Saddle Point Attack in Byzantine-Robust Distributed Learning Dong Yin Yudong Chen Kannan Ramchandran Peter L. Bartlett FedML 32 97 0 14 Jun 2018
On Landscape of Lagrangian Functions and Stochastic Search for Constrained Nonconvex Optimization Zhehui Chen Xingguo Li Lin F. Yang Jarvis Haupt T. Zhao 10 4 0 13 Jun 2018
Towards Riemannian Accelerated Gradient Methods Hongyi Zhang S. Sra 19 53 0 07 Jun 2018
Implicit regularization and solution uniqueness in over-parameterized matrix sensing Kelly Geyer Anastasios Kyrillidis A. Kalev 27 4 0 06 Jun 2018
Algorithmic Regularization in Learning Deep Homogeneous Models: Layers are Automatically Balanced S. Du Wei Hu J. Lee MLT 40 237 0 04 Jun 2018
Provably convergent acceleration in factored gradient descent with applications in matrix sensing Tayo Ajayi David Mildebrath Anastasios Kyrillidis Shashanka Ubaru Georgios Kollias K. Bouchard 18 1 0 01 Jun 2018
Nonlinear Inductive Matrix Completion based on One-layer Neural Networks Kai Zhong Zhao Song Prateek Jain Inderjit S. Dhillon 9 6 0 26 May 2018
How Much Restricted Isometry is Needed In Nonconvex Matrix Recovery? Richard Y. Zhang C. Josz Somayeh Sojoudi Javad Lavaei 22 42 0 25 May 2018
$Simple and practical algorithms for $\ell_p$-norm low-rank approximation$ Simple and practical algorithms for $\ell_p$ -norm low-rank approximation Anastasios Kyrillidis 15 5 0 24 May 2018
How Many Samples are Needed to Estimate a Convolutional or Recurrent Neural Network? S. Du Yining Wang Xiyu Zhai Sivaraman Balakrishnan Ruslan Salakhutdinov Aarti Singh SSL 21 57 0 21 May 2018
Improved Learning of One-hidden-layer Convolutional Neural Networks with Overlaps S. Du Surbhi Goel MLT 30 17 0 20 May 2018
The Global Optimization Geometry of Shallow Linear Neural Networks Zhihui Zhu Daniel Soudry Yonina C. Eldar M. Wakin ODL 20 36 0 13 May 2018
Convergence guarantees for a class of non-convex and non-smooth optimization problems K. Khamaru Martin J. Wainwright 17 72 0 25 Apr 2018
Notes on computational-to-statistical gaps: predictions using statistical physics Afonso S. Bandeira Amelia Perry Alexander S. Wein AI4CE 25 57 0 29 Mar 2018
Non-Convex Matrix Completion Against a Semi-Random Adversary Yu Cheng Rong Ge AAML 36 24 0 28 Mar 2018
An Analysis of the t-SNE Algorithm for Data Visualization Sanjeev Arora Wei Hu Pravesh Kothari 16 148 0 05 Mar 2018
How to Start Training: The Effect of Initialization and Architecture Boris Hanin David Rolnick 13 253 0 05 Mar 2018
Fast and Sample Efficient Inductive Matrix Completion via Multi-Phase Procrustes Flow Xiao Zhang S. Du Quanquan Gu 26 24 0 03 Mar 2018
Static and Dynamic Robust PCA and Matrix Completion: A Review Namrata Vaswani Praneeth Narayanamurthy 24 73 0 01 Mar 2018
Smoothed analysis for low-rank solutions to semidefinite programs in quadratic penalty form Srinadh Bhojanapalli Nicolas Boumal Prateek Jain Praneeth Netrapalli 29 44 0 01 Mar 2018
On the Sublinear Convergence of Randomly Perturbed Alternating Gradient Descent to Second Order Stationary Solutions Songtao Lu Mingyi Hong Zhengdao Wang 13 4 0 28 Feb 2018
Harnessing Structures in Big Data via Guaranteed Low-Rank Matrix Estimation Yudong Chen Yuejie Chi 18 171 0 23 Feb 2018
Spurious Valleys in Two-layer Neural Network Optimization Landscapes Luca Venturi Afonso S. Bandeira Joan Bruna 32 74 0 18 Feb 2018
Gradient descent with identity initialization efficiently learns positive definite linear transformations by deep residual networks Peter L. Bartlett D. Helmbold Philip M. Long 36 116 0 16 Feb 2018
Learning Compact Neural Networks with Regularization Samet Oymak MLT 41 39 0 05 Feb 2018