Implicit Regularization in Nonconvex Statistical Estimation: Gradient Descent Converges Linearly for Phase Retrieval, Matrix Completion, and Blind Deconvolution

28 November 2017

Papers citing "Implicit Regularization in Nonconvex Statistical Estimation: Gradient Descent Converges Linearly for Phase Retrieval, Matrix Completion, and Blind Deconvolution"

42 / 42 papers shown

Title
Euclidean Distance Matrix Completion via Asymmetric Projected Gradient Descent Yicheng Li Xinghua Sun 39 0 0 28 Apr 2025
Leave-One-Out Analysis for Nonconvex Robust Matrix Completion with General Thresholding Functions Tianming Wang Ke Wei 33 1 0 28 Jul 2024
Provably Accelerating Ill-Conditioned Low-rank Estimation via Scaled Gradient Descent, Even with Overparameterization Cong Ma Xingyu Xu Tian Tong Yuejie Chi 18 9 0 09 Oct 2023
Deflated HeteroPCA: Overcoming the curse of ill-conditioning in heteroskedastic PCA Yuchen Zhou Yuxin Chen 40 4 0 10 Mar 2023
$Approximate message passing from random initialization with applications to $\mathbb{Z}_{2}$ synchronization$ Approximate message passing from random initialization with applications to $\mathbb{Z}_{2}$ synchronization Gen Li Wei Fan Yuting Wei 26 10 0 07 Feb 2023
Learning Transition Operators From Sparse Space-Time Samples C. Kümmerle Mauro Maggioni Sui Tang 26 1 0 01 Dec 2022
Nonconvex Matrix Factorization is Geodesically Convex: Global Landscape Analysis for Fixed-rank Matrix Optimization From a Riemannian Perspective Yuetian Luo Nicolas García Trillos 24 6 0 29 Sep 2022
Gradient-Free Methods for Deterministic and Stochastic Nonsmooth Nonconvex Optimization Tianyi Lin Zeyu Zheng Michael I. Jordan 59 52 0 12 Sep 2022
Sudakov-Fernique post-AMP, and a new proof of the local convexity of the TAP free energy Michael Celentano 46 20 0 19 Aug 2022
Variational Bayesian inference for CP tensor completion with side information S. Budzinskiy N. Zamarashkin 16 1 0 24 Jun 2022
Robust Matrix Completion with Heavy-tailed Noise Bingyan Wang Jianqing Fan 21 4 0 09 Jun 2022
Model-Based Reinforcement Learning for Offline Zero-Sum Markov Games Yuling Yan Gen Li Yuxin Chen Jianqing Fan OffRL 31 10 0 08 Jun 2022
On Asymptotic Linear Convergence of Projected Gradient Descent for Constrained Least Squares Trung Vu Raviv Raich 27 13 0 22 Dec 2021
OMASGAN: Out-of-Distribution Minimum Anomaly Score GAN for Sample Generation on the Boundary Nikolaos Dionelis Mehrdad Yaghoobi Sotirios A. Tsaftaris OODD 23 6 0 28 Oct 2021
Tensor train completion: local recovery guarantees via Riemannian optimization S. Budzinskiy N. Zamarashkin 55 14 0 08 Oct 2021
Nonconvex Factorization and Manifold Formulations are Almost Equivalent in Low-rank Matrix Optimization Yuetian Luo Xudong Li Anru R. Zhang 33 9 0 03 Aug 2021
Small random initialization is akin to spectral learning: Optimization and generalization guarantees for overparameterized low-rank matrix reconstruction Dominik Stöger Mahdi Soltanolkotabi ODL 42 75 0 28 Jun 2021
GNMR: A provable one-line algorithm for low rank matrix recovery Pini Zilber B. Nadler 48 14 0 24 Jun 2021
Spectral Methods for Data Science: A Statistical Perspective Yuxin Chen Yuejie Chi Jianqing Fan Cong Ma 42 165 0 15 Dec 2020
Recursive Importance Sketching for Rank Constrained Least Squares: Algorithms and High-order Convergence Yuetian Luo Wen Huang Xudong Li Anru R. Zhang 23 15 0 17 Nov 2020
Low-Rank Matrix Recovery with Scaled Subgradient Methods: Fast and Robust Convergence Without the Condition Number Tian Tong Cong Ma Yuejie Chi 21 55 0 26 Oct 2020
Near-Optimal Performance Bounds for Orthogonal and Permutation Group Synchronization via Spectral Methods Shuyang Ling 34 34 0 12 Aug 2020
Second-Order Information in Non-Convex Stochastic Optimization: Power and Limitations Yossi Arjevani Y. Carmon John C. Duchi Dylan J. Foster Ayush Sekhari Karthik Sridharan 87 53 0 24 Jun 2020
Uncertainty quantification for nonconvex tensor completion: Confidence intervals, heteroscedasticity and optimality Changxiao Cai H. Vincent Poor Yuxin Chen 13 23 0 15 Jun 2020
Breaking the Sample Size Barrier in Model-Based Reinforcement Learning with a Generative Model Gen Li Yuting Wei Yuejie Chi Yuxin Chen 34 124 0 26 May 2020
Accelerating Ill-Conditioned Low-Rank Matrix Estimation via Scaled Gradient Descent Tian Tong Cong Ma Yuejie Chi 27 115 0 18 May 2020
The estimation error of general first order methods Michael Celentano Andrea Montanari Yuchen Wu 14 44 0 28 Feb 2020
$Depth Descent Synchronization in $\mathrm{SO}(D)$$ Depth Descent Synchronization in $\mathrm{SO}(D)$ Tyler Maunu Gilad Lerman MDE 37 2 0 13 Feb 2020
Analysis of the Optimization Landscapes for Overcomplete Representation Learning Qing Qu Yuexiang Zhai Xiao Li Yuqian Zhang Zhihui Zhu 22 9 0 05 Dec 2019
Manifold Gradient Descent Solves Multi-Channel Sparse Blind Deconvolution Provably and Efficiently Laixi Shi Yuejie Chi 30 26 0 25 Nov 2019
$Policy Optimization for $\mathcal{H}_2$ Linear Control with $\mathcal{H}_\infty$ Robustness Guarantee: Implicit Regularization and Global Convergence$ Policy Optimization for $\mathcal{H}_2$ Linear Control with $\mathcal{H}_\infty$ Robustness Guarantee: Implicit Regularization and Global Convergence Kaipeng Zhang Bin Hu Tamer Basar 24 119 0 21 Oct 2019
Short-and-Sparse Deconvolution -- A Geometric Approach Yenson Lau Qing Qu Han-Wen Kuo Pengcheng Zhou Yuqian Zhang John N. Wright 19 29 0 28 Aug 2019
Gradient Descent Maximizes the Margin of Homogeneous Neural Networks Kaifeng Lyu Jian Li 52 322 0 13 Jun 2019
A Priori Estimates of the Population Risk for Residual Networks E. Weinan Chao Ma Qingcan Wang UQCV 37 61 0 06 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
Blind Over-the-Air Computation and Data Fusion via Provable Wirtinger Flow Jialin Dong Yuanming Shi Z. Ding 9 59 0 12 Nov 2018
Regularization Matters: Generalization and Optimization of Neural Nets v.s. their Induced Kernel Colin Wei J. Lee Qiang Liu Tengyu Ma 23 245 0 12 Oct 2018
Stochastic Gradient/Mirror Descent: Minimax Optimality and Implicit Regularization Navid Azizan B. Hassibi 21 61 0 04 Jun 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
The Projected Power Method: An Efficient Algorithm for Joint Alignment from Pairwise Differences Yuxin Chen Emmanuel Candes 40 92 0 19 Sep 2016
On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima N. Keskar Dheevatsa Mudigere J. Nocedal M. Smelyanskiy P. T. P. Tang ODL 308 2,890 0 15 Sep 2016
Median-Truncated Nonconvex Approach for Phase Retrieval with Outliers Huishuai Zhang Yuejie Chi Yingbin Liang 22 55 0 11 Mar 2016