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A vast majority of machine learning algorithms train their models and perform inference by solving optimization problems.
A Practical Algorithm for the Determination of Phase from Image and Diffraction Plane Pictures
R. W. Gerchberg and W. Owen Saxton · 1972
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The diameters of octahedra
Boris Sergeevich Kashin · 1975
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Maximum Likelihood from Incomplete Data via the EM Algorithm
Arthur P. Dempster, Nan M. Laird, and Donald B. Rubin · 1977
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Robust Generalized M-estimates for Autoregressive Parameters: Small-sample Behavior and Applications
R. Douglas Martin and Judy Zeh · 1978
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Random Sample Consensus: A Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography
Martin A. Fischler and Robert C. Bolles · 1981
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Least squares quantization in PCM
Stuart P. Lloyd · 1982
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On the Convergence Properties of the EM Algorithm
C.-F. Jeff Wu · 1983
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Least Median of Squares Regression
Peter J. Rousseeuw · 1984
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Robust Regression and Outlier Detection
Peter J. Rousseeuw and Annick M. Leroy · 1987
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Robust time series analysis: A survey
Norbert Stockinger and Rudolf Dutter · 1987
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On the Convergence of the Coordinate Descent Method for Convex Differentiable Minimization
Zhi-Quan Luo and Paul Tseng · 1992
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Error bounds and convergence analysis of feasible descent methods: A general approach
Zhi-Quan Luo and Paul Tseng · 1993
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Sparse approximate solutions to linear systems
Balas Kausik Natarajan · 1995
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Matrix Computations
Gene H. Golub and Charles F. Van Loan · 1996
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Numerical Optimization , volume 2
Stephen J Wright and Jorge Nocedal · 1999
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Introductory Lectures on Convex Optimization: A Basic Course
Yurii Nesterov · 2003
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Microarray Analysis of Gene Expression in the Kidneys of New- and Post-Onset Diabetic NOD Mice
Karen H.S. Wilson, Sarah E. Eckenrode, Quan-Zhen Li, Qing-Guo Ruan, Ping Yang, Jing-Da Shi, Abdoreza Davoodi-Semiromi, Richard A. McIndoe, Byron P. Croker, and Jin-Xiong She · 2003
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Convex Optimization
Stephen Boyd and Lieven Vandenberghe · 2004
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Decoding by Linear Programming
Emmanuel Candès and Terence Tao · 2005
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Stable Signal Recovery from Incomplete and Inaccurate Measurements
Emmanuel J. Candès, Justin K. Romberg, and Terence Tao · 2006
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Compressed Sensing
David L. Donoho · 2006
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Robust Statistics: Theory and Methods
Ricardo A. Maronna, R. Douglas Martin, and Victor J. Yoha · 2006
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Cubic regularization of Newton method and its global performance
Yurii Nesterov and B.T. Polyak · 2006
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Exact Reconstruction of Sparse Signals via Nonconvex Minimization
Rick Chartrand · 2007
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Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
Joel A. Tropp and Anna C. Gilbert · 2007
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A Simple Proof of the Restricted Isometry Property for Random Matrices
Richard Baraniuk, Mark Davenport, Ronald DeVore, and Michael Wakin · 2008
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The Restricted Isometry Property and Its Implications for Compressed Sensing
Emmanuel J. Candès · 2008
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Robust Estimation of the Vector Autoregressive Model by a Least Trimmed Squares Procedure
Christophe Croux and Kristel Joossens · 2008
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Efficient Projections onto the ℓ 1 \ell_{1} -Ball for Learning in High Dimensions
John Duchi, Shai Shalev-Shwartz, Yoram Singer, and Tushar Chandra · 2008
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LIBLINEAR: A Library for Large Linear Classification
Rong-En Fan, Kai-Wei Chang, Cho-Jui Hsieh, Xiang-Rui Wang, and Chih-Jen Lin · 2008
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A-DNA and B-DNA: Comparing Their Historical X-ray Fiber Diffraction Images
Amand A. Lucas · 2008
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Rank Minimization via Online Learning
Raghu Meka, Prateek Jain, Constantine Caramanis, and Inderjit Dhillon · 2008
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CoSaMP: Iterative Signal Recovery from Incomplete and Inaccurate Samples
Deanna Needell and Joel A. Tropp · 2008
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Large-scale Parallel Collaborative Filtering for the Netflix Prize
Yunhong Zhou, Dennis Wilkinson, Robert Schreiber, and Rong Pan · 2008
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Exact Matrix Completion via Convex Optimization
Emmanuel J. Candès and Benjamin Recht · 2009
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The power of convex relaxation: Near-optimal matrix completion
Emmanuel J. Candès and Terence Tao · 2009
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Compressed Sensing and Best k k -term Approximation
Albert Cohen, Wolfgang Dahmen, and Ronald DeVore · 2009
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Message Passing Algorithms for Compressed Sensing: I. Motivation and Construction
David L. Donoho, Arian Maleki, and Andrea Montanari · 2009
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Sparsest solutions of underdetermined linear systems via ℓ q \ell_{q} -minimization for 0 < q ≤ 1 0<q\leq 1
Simon Foucart and Ming-Jun Lai · 2009
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Gradient Descent with Sparsification: An iterative algorithm for sparse recovery with restricted isometry property
Rahul Garg and Rohit Khandekar · 2009
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Robust Statistics
Peter J. Huber and Elvezio M. Ronchetti · 2009
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Matrix Factorization Techniques for. Recommender Systems
Yehuda Koren, Robert Bell, and Chris Volinsky · 2009
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Robust Face Recognition via Sparse Representation
John Wright, Alan Y. Yang, Arvind Ganesh, S. Shankar Sastry, and Yi Ma · 2009
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A Singular Value Thresholding Algorithm for Matrix Completion
Jian-Feng Cai, Emmanuel J. Candès, and Zuowei Shen · 2010
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A Note on Guaranteed Sparse Recovery via ℓ 1 \ell_{1} -minimization
Simon Foucart · 2010
Cited alongside, same era.
Guaranteed Rank Minimization via Singular Value Projections
Prateek Jain, Raghu Meka, and Inderjit Dhillon · 2010
Cited alongside, same era.
Matrix Completion from a Few Entries
Raghunandan H. Keshavan, Andrea Montanari, and Sewoong Oh · 2010
Cited alongside, same era.
ADMiRA: Atomic Decomposition for Minimum Rank Approximation
Kiryung Lee and Yoram Bresler · 2010
Cited alongside, same era.
Restricted Eigenvalue Properties for Correlated Gaussian Designs
Garvesh Raskutti, Martin J. Wainwright, and Bin Yu · 2010
Cited alongside, same era.
Guaranteed Minimum Rank Solutions to Linear Matrix Equations via Nuclear Norm Minimization
Benjamin Recht, Maryam Fazel, and Pablo A. Parrilo · 2010
Cited alongside, same era.
New constructions of RIP matrices with fast multiplication and fewer rows
Jelani Nelson, Eric Price, and Mary Wootters · 2014
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Alternating Minimization for Mixed Linear Regression
Xinyang Yi, Constantine Caramanis, and Sujay Sanghavi · 2014
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Robust Regression via Hard Thresholding
Kush Bhatia, Prateek Jain, and Purushottam Kar · 2015
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Convex Optimization: Algorithms and Complexity
Sebastien Bubeck · 2015
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Phase Retrieval via Wirtinger Flow: Theory and Algorithms
Emmanuel J. Candès, Xiaodong Li, and Mahdi Soltanolkotabi · 2015
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Local and global optimality of LP minimization for sparse recovery
Laming Chen and Yuantao Gu · 2015
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Sampling and Reconstructing Signals From a Union of Linear Subspaces
Thomas Blumensath · 2011
Cited alongside, same era.
Explicit constructions of RIP matrices and related problems
Jean Bourgain, Stephen Dilworth, Kevin Ford, Sergei Konyagin, and Denka Kutzarova · 2011
Cited alongside, same era.
Hard Thresholding Pursuit: an Algorithm for Compressive Sensing
Simon Foucart · 2011
Cited alongside, same era.
Convergence of Fixed-Point Continuation Algorithms for Matrix Rank Minimization
Donald Goldfarb and Shiqian Ma · 2011
Cited alongside, same era.
Orthogonal Matching Pursuit with Replacement
Prateek Jain, Ambuj Tewari, and Inderjit S. Dhillon · 2011
Cited alongside, same era.
On Learning Discrete Graphical Models using Greedy Methods
Ali Jalali, Christopher C Johnson, and Pradeep D Ravikumar · 2011
Cited alongside, same era.
The Loss Surfaces of Multilayer Networks
Anna Choromanska, Mikael Hena, Michael Mathieu, Gérard Ben Arous, and Yann LeCun · 2015
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Escaping From Saddle Points - Online Stochastic Gradient for Tensor Decomposition
Rong Ge, Furong Huang, Chi Jin, and Yang Yuan · 2015
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Sparse and Spurious: Dictionary Learning With Noise and Outliers
Rémi Gribonval, Rodolphe Jenatton, and Francis Bach · 2015
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Fast Exact Matrix Completion with Finite Samples
Prateek Jain and Praneeth Netrapalli · 2015
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Alternating Minimization for Regression Problems with Vector-valued Outputs
Prateek Jain and Ambuj Tewari · 2015
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Sharp Time-Data Tradeoffs for Linear Inverse Problems
Samet Oymak, Benjamin Recht, and Mahdi Soltanolkotabi · 2015
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When Are Nonconvex Problems Not Scary?
Ju Sun, Qing Qu, and John Wright · 2015
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Guaranteed Matrix Completion via Non-convex Factorization
Ruoyu Sun and Zhi-Quan Lu · 2015
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High Dimensional EM Algorithm: Statistical Optimization and Asymptotic Normality
Zhaoran Wang, Quanquan Gu, Yang Ning, and Han Liu · 2015
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Statistical and computational guarantees for the Baum-Welch algorithm
Fanny Yang, Sivaraman Balakrishnan, and Martin J. Wainwright · 2015
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Regularized EM Algorithms: A Unified Framework and Statistical Guarantees
Xinyang Yi and Constantine Caramanis · 2015
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Recent advances in trust region algorithms
Ya-Xiang Yuan · 2015
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Learning Sparsely Used Overcomplete Dictionaries via Alternating Minimization
Alekh Agarwal, Animashree Anandkumar, Prateek Jain, and Praneeth Netrapalli · 2016
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Efficient approaches for escaping higher order saddle points in non-convex optimization
Animashree Anandkumar and Rong Ge · 2016
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Convergence of an Alternating Maximization Procedure
Andreas Andresen and Vladimir Spokoiny · 2016
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Reinforcement Learning of POMDPs using Spectral Methods
Kamyar Azizzadenesheli, Alessandro Lazaric, and Anima Anandkumar · 2016
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Nonlinear Programming
Dimitri P. Bertsekas · 2016
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Matrix Completion with Column Manipulation: Near-Optimal Sample-Robustness-Rank Tradeoffs
Yudong Chen, Huan Xu, Constantine Caramanis, and Sujay Sanghavi · 2016
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Matrix Completion has No Spurious Local Minimum
Rong Ge, Jason D. Lee, and Tengyu Ma · 2016
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Statistical Learning with Sparsity: The Lasso and Generalizations
Trevor Hastie, Robert Tibshirani, and Martin Wainwright · 2016
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Gradient Descent Only Converges to Minimizers
Jason D. Lee, Max Simchowitz, Michael I. Jordan, and Benjamin Recht · 2016
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Fast Stochastic Methods for Nonsmooth Nonconvex Optimization
Sashank Reddi, Ahmed Hefny, Suvrit Sra, Barnabas Poczos, and Alexander J. Smola · 2016
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Training Input-Output Recurrent Neural Networks through Spectral Methods
Hanie Sedghi and Anima Anandkumar · 2016
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Finding Approximate Local Minima Faster than Gradient Descent
Naman Agarwal, Zeyuan Allen-Zhu, Brian Bullins, Elad Hazan, and Tengyu Ma · 2017
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Statistical Guarantees for the EM Algorithm: From Population to Sample-based Analysis
Sivaraman Balakrishnan, Martin J. Wainwright, and Bin Yu · 2017
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Consistent Robust Regression
Kush Bhatia, Prateek Jain, Parameswaran Kamalaruban, and Purushottam Kar · 2017
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Globally Optimal Gradient Descent for a ConvNet with Gaussian Inputs
Alon Brutzkus and Amir Globerson · 2017
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“Convex Until Proven Guilty”: Dimension-Free Acceleration of Gradient Descent on Non-Convex Functions
Yair Carmon, John C. Duchi, Oliver Hinder, and Aaron Sidford · 2017
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Nearly-optimal Robust Matrix Completion
Yeshwanth Cherapanamjeri, Kartik Gupta, and Prateek Jain · 2017
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Learning Depth-Three Neural Networks in Polynomial Time
Surbhi Goel and Adam Klivans · 2017
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The Restricted Isometry Property of Subsampled Fourier Matrices
Ishay Haviv and Oded Regev · 2017
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How to Escape Saddle Points Efficiently
Chi Jin, Rong Ge, Praneeth Netrapalli, Sham M. Kakade, and Michael I. Jordan · 2017
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Convergence Analysis of Two-layer Neural Networks with ReLU Activation
Yuanzhi Li and Yang Yuan · 2017
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A Hitting Time Analysis of Stochastic Gradient Langevin Dynamics
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Recovery Guarantees for One-hidden-layer Neural Networks
Kai Zhong, Zhao Song, Prateek Jain, Peter L. Bartlett, and Inderjit S. Dhillon · 2017
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Exact recoverability from dense corrupted observations via L1 minimization
Nam H. Nguyen and Trac D. Tran · 2058
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Robust Lasso With Missing and Grossly Corrupted Observations
Nam H Nguyen and Trac D Tran · 2058
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