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A popular approach for estimating an unknown signal from noisy, linear measurements is via solving a so called \emph{regularized M-estimator}, which minimizes a weighted combination of a convex loss function and of a convex (typically, non-smooth) regularizer.
On general minimax theorems
Maurice Sion et al · 1958
Earlier work this paper cites.
Cox’s regression model for counting processes: a large sample study
Per Kragh Andersen and Richard D Gill · 1982
Earlier work this paper cites.
Some inequalities for gaussian processes and applications
Yehoram Gordon · 1985
Earlier work this paper cites.
On Milman’s inequality and random subspaces which escape through a mesh in ℝ n \mathbb{R}^{n}
Yehoram Gordon · 1988
Earlier work this paper cites.
Probability in Banach Spaces: isoperimetry and processes
Michel Ledoux and Michel Talagrand · 1991
Earlier work this paper cites.
Minimax risk overl p-balls forl p-error
David L Donoho and Iain M Johnstone · 1994
Earlier work this paper cites.
Large sample estimation and hypothesis testing
Whitney K Newey and Daniel McFadden · 1994
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Regression shrinkage and selection via the lasso
Robert Tibshirani · 1996
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Convex analysis
R Tyrell Rockafellar · 1997
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High-dimensional data analysis: The curses and blessings of dimensionality
David L Donoho et al · 2000
Earlier work this paper cites.
Near-optimal signal recovery from random projections: Universal encoding strategies?
Emmanuel J Candes and Terence Tao · 2006
Earlier work this paper cites.
High-dimensional centrally symmetric polytopes with neighborliness proportional to dimension
David L Donoho · 2006
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Sparse reconstruction by convex relaxation: Fourier and gaussian measurements
Mark Rudelson and Roman Vershynin · 2006
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The dantzig selector: Statistical estimation when p is much larger than n
Emmanuel Candes and Terence Tao · 2007
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Generalized entropy power inequalities and monotonicity properties of information
Mokshay Madiman and Andrew Barron · 2007
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Statistical decision theory: estimation, testing, and selection
Friedrich Liese and Klaus-J Miescke · 2008
Earlier work this paper cites.
Simultaneous analysis of lasso and dantzig selector
Peter J Bickel, YaÕacov Ritov, and Alexandre B Tsybakov · 2009
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Message-passing algorithms for compressed sensing
David L Donoho, Arian Maleki, and Andrea Montanari · 2009
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Counting faces of randomly projected polytopes when the projection radically lowers dimension
David Donoho and Jared Tanner · 2009
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Observed universality of phase transitions in high-dimensional geometry, with implications for modern data analysis and signal processing
David Donoho and Jared Tanner · 2009
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A single-letter characterization of optimal noisy compressed sensing
Dongning Guo, Dror Baron, and Shlomo Shamai · 2009
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Asymptotic analysis of map estimation via the replica method and compressed sensing
Sundeep Rangan, Vivek Goyal, and Alyson K Fletcher · 2009
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Variational analysis
R Tyrrell Rockafellar and Roger J-B Wets · 2009
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Block-length dependent thresholds in block-sparse compressed sensing
Mihailo Stojnic · 2009
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Various thresholds for ℓ 1 \ell_{1} -optimization in compressed sensing
Mihailo Stojnic · 2009
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Sharp thresholds for high-dimensional and noisy sparsity recovery using-constrained quadratic programming (lasso)
Martin J Wainwright · 2009
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Structured sparsity-inducing norms through submodular functions
Francis R Bach · 2010
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Probability: theory and examples
Rick Durrett · 2010
Earlier work this paper cites.
Statistical mechanical analysis of a typical reconstruction limit of compressed sensing
Yoshiyuki Kabashima, Tadashi Wadayama, and Toshiyuki Tanaka · 2010
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New null space results and recovery thresholds for matrix rank minimization
Samet Oymak and Babak Hassibi · 2010
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Introduction to the non-asymptotic analysis of random matrices
Roman Vershynin · 2010
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Square-root lasso: pivotal recovery of sparse signals via conic programming
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The dynamics of message passing on dense graphs, with applications to compressed sensing
Mohsen Bayati and Andrea Montanari · 2011
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Introduction to compressed sensing
Mark A Davenport, Marco F Duarte, Yonina C Eldar, and Gitta Kutyniok · 2011
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Estimation with norm regularization
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Corrupted sensing: Novel guarantees for separating structured signals
Rina Foygel and Lester Mackey · 2014
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Sparse recovery under weak moment assumptions
Guillaume Lecué and Shahar Mendelson · 2014
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Michael B McCoy, Volkan Cevher, Quoc Tran Dinh, Afsaneh Asaei, and Leonetta Baldassarre · 2014
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Sharp recovery bounds for convex demixing, with applications
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Estimating structured signals in sparse noise: A precise noise sensitivity analysis
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Applications of the lindeberg principle in communications and statistical learning
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Null space conditions and thresholds for rank minimization
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Precise stability phase transitions for minimization: A unified geometric framework
Weiyu Xu and Babak Hassibi · 2011
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The lasso risk for gaussian matrices
Mohsen Bayati and Andrea Montanari · 2012
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The convex geometry of linear inverse problems
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Simple error bounds for regularized noisy linear inverse problems
Christos Thrampoulidis, Samet Oymak, and Babak Hassibi · 2014
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Convex recovery of a structured signal from independent random linear measurements
Joel A Tropp · 2014
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Estimation in high dimensions: a geometric perspective
Roman Vershynin · 2014
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Analysis of regularized ls reconstruction and random matrix ensembles in compressed sensing
Mikko Vehkapera, Yoshiyuki Kabashima, and Saptarshi Chatterjee · 2014
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Structured regularizers for high-dimensional problems: Statistical and computational issues
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Asymptotic Geometric Analysis, Part I
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Robustness in sparse linear models: relative efficiency based on robust approximate message passing
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Universality in polytope phase transitions and message passing algorithms
Mohsen Bayati, Marc Lelarge, Andrea Montanari, et al · 2015
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Variance breakdown of huber (m)-estimators: n/p \rightarrow m\in (1,\infty)
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On the impact of predictor geometry on the performance on high-dimensional ridge-regularized generalized robust regression estimators
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Universality laws for randomized dimension reduction, with applications
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Beyond sub-gaussian measurements: High-dimensional structured estimation with sub-exponential designs
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The lasso with non-linear measurements is equivalent to one with linear measurements
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Ber analysis of the box relaxation for bpsk signal recovery
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Regularized linear regression: A precise analysis of the estimation error
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Precise error analysis of the lasso
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Asymptotically exact error analysis for the generalized ℓ 2 2 \ell_{2}^{2} -lasso
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