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Iterative thresholding algorithms seek to optimize a differentiable objective function over a sparsity or rank constraint by alternating between gradient steps that reduce the objective, and thresholding steps that enforce the constraint.
Regression shrinkage and selection via the lasso
Robert Tibshirani · 1996
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Adaptive estimation of a quadratic functional by model selection
Beatrice Laurent and Pascal Massart · 2000
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Variable selection via nonconcave penalized likelihood and its oracle properties
Jianqing Fan and Runze Li · 2001
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Exact reconstruction of sparse signals via nonconvex minimization
Rick Chartrand · 2007
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Simultaneous analysis of lasso and dantzig selector
Peter J Bickel, Ya’acov Ritov, Alexandre B Tsybakov, et al · 2009
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Iterative hard thresholding for compressed sensing
Thomas Blumensath and Mike E Davies · 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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A typical reconstruction limit for compressed sensing based on ℓ p \ell_{p} -norm minimization
Yoshiyuki Kabashima, Tadashi Wadayama, and Toshiyuki Tanaka · 2009
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A unified framework for high-dimensional analysis of M-estimators with decomposable regularizers
Sahand Negahban, Bin Yu, Martin J Wainwright, and Pradeep K Ravikumar · 2009
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Restricted eigenvalue properties for correlated gaussian designs
Garvesh Raskutti, Martin J Wainwright, and Bin Yu · 2010
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Nearly unbiased variable selection under minimax concave penalty
Cun-Hui Zhang · 2010
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Recipes on hard thresholding methods
Anastasios Kyrillidis and Volkan Cevher · 2011
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An unconstrained \ \backslash ell_q minimization with 0q \ \backslash leq1 for sparse solution of underdetermined linear systems
Ming-Jun Lai and Jingyue Wang · 2011
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Accelerated iterative hard thresholding
Thomas Blumensath · 2012
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Regularized M-estimators with nonconvexity: Statistical and algorithmic theory for local optima
Po-Ling Loh and Martin J Wainwright · 2013
Lower bounds on the performance of polynomial-time algorithms for sparse linear regression
Yuchen Zhang, Martin J Wainwright, and Michael I Jordan · 2014
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Robust regression via hard thresholding
Kush Bhatia, Prateek Jain, and Purushottam Kar · 2015
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Yudong Chen and Martin J Wainwright · 2015
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Does ℓ p \ell_{p} -minimization outperform ℓ 1 \ell_{1} -minimization?
Le Zheng, Arian Maleki, Haolei Weng, Xiaodong Wang, and Teng Long · 2015
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Optimal rates of convergence for noisy sparse phase retrieval via thresholded Wirtinger flow
T Tony Cai, Xiaodong Li, and Zongming Ma · 2016
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On iterative hard thresholding methods for high-dimensional M-estimation
Prateek Jain, Ambuj Tewari, and Purushottam Kar · 2014
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Matrix recipes for hard thresholding methods
Anastasios Kyrillidis and Volkan Cevher · 2014
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Proximal algorithms
Neal Parikh, Stephen Boyd, et al · 2014
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Structured sparse regression via greedy hard thresholding
Prateek Jain, Nikhil Rao, and Inderjit S Dhillon · 2016
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Gradient descent with nonconvex constraints: local concavity determines convergence
Rina Foygel Barber and Wooseok Ha · 2017
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IHT dies hard: provable accelerated iterative hard thresholding
Rajiv Khanna and Anastasios Kyrillidis · 2017
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Linear convergence of stochastic iterative greedy algorithms with sparse constraints
Nam Nguyen, Deanna Needell, and Tina Woolf · 2017
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