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The Lasso is a popular regression method for high-dimensional problems in which the number of parameters $\theta_1,\dots,\theta_N$, is larger than the number $n$ of samples: $N>n$.
Estimation of the mean of a multivariate normal distribution
Charles M Stein · 1981
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Some inequalities for Gaussian processes and applications
Yehoram Gordon · 1985
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On Milman’s inequality and random subspaces which escape through a mesh in ℝ n \mathbb{R}^{n}
Yehoram Gordon · 1988
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Minimax risk over ℓ p \ell_{p} -balls for ℓ q \ell_{q} -error
David L Donoho and Iain M Johnstone · 1994
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Ideal spatial adaptation by wavelet shrinkage
David L Donoho and Jain M Johnstone · 1994
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Examples of basis pursuit
Scott Chen and David L Donoho · 1995
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Regression shrinkage and selection via the lasso
Robert Tibshirani · 1996
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Function estimation and gaussian sequence models
Iain M Johnstone · 2002
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Convex analysis in general vector spaces
Constantin Zalinescu · 2002
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The estimation of prediction error: covariance penalties and cross-validation
Bradley Efron · 2004
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Decoding by linear programming
Emmanuel J Candes and Terence Tao · 2005
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Neighborliness of randomly projected simplices in high dimensions
David L Donoho and Jared Tanner · 2005
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High-dimensional centrally symmetric polytopes with neighborliness proportional to dimension
David L Donoho · 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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Optimal transport: old and new
Cédric Villani · 2008
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Simultaneous analysis of Lasso and Dantzig selector
Peter J Bickel, Ya’acov 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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On the conditions used to prove oracle results for the lasso
Sara A Van De Geer, Peter Bühlmann, et al · 2009
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Recovery thresholds for ℓ 1 \ell_{1} optimization in binary compressed sensing
Mihailo Stojnic · 2010
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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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Statistics for high-dimensional data: methods, theory and applications
Peter Bühlmann and Sara Van De Geer · 2011
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The noise-sensitivity phase transition in compressed sensing
David L Donoho, Arian Maleki, and Andrea Montanari · 2011
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Generalized approximate message passing for estimation with random linear mixing
Sundeep Rangan · 2011
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Minimax rates of estimation for high-dimensional linear regression over ℓ q \ell_{q} -balls
Garvesh Raskutti, Martin J Wainwright, and Bin Yu · 2011
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The lasso risk for gaussian matrices
Mohsen Bayati and Andrea Montanari · 2012
On the rate of convergence in wasserstein distance of the empirical measure
Nicolas Fournier and Arnaud Guillin · 2015
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Convex analysis
Ralph Tyrell Rockafellar · 2015
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Compressive phase retrieval via generalized approximate message passing
Philip Schniter and Sundeep Rangan · 2015
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Regularized linear regression: A precise analysis of the estimation error
Christos Thrampoulidis, Samet Oymak, and Babak Hassibi · 2015
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Convex recovery of a structured signal from independent random linear measurements
Joel A Tropp · 2015
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The mutual information in random linear estimation
Jean Barbier, Mohamad Dia, Nicolas Macris, and Florent Krzakala · 2016
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Regularization techniques for learning with matrices
Sham M Kakade, Shai Shalev-Shwartz, and Ambuj Tewari · 2012
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A unified framework for high-dimensional analysis of m m -estimators with decomposable regularizers
Sahand N Negahban, Pradeep Ravikumar, Martin J Wainwright, Bin Yu, et al · 2012
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Degrees of freedom in lasso problems
Ryan J Tibshirani, Jonathan Taylor, et al · 2012
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Estimating lasso risk and noise level
Mohsen Bayati, Murat A Erdogdu, and Andrea Montanari · 2013
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Concentration inequalities: A nonasymptotic theory of independence
Stéphane Boucheron, Gábor Lugosi, and Pascal Massart · 2013
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Noureddine El Karoui · 2013
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High dimensional robust m-estimation: Asymptotic variance via approximate message passing
David Donoho and Andrea Montanari · 2016
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Non-negative principal component analysis: Message passing algorithms and sharp asymptotics
Andrea Montanari and Emile Richard · 2016
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The replica-symmetric prediction for compressed sensing with gaussian matrices is exact
Galen Reeves and Henry D Pfister · 2016
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State evolution for approximate message passing with non-separable functions
Raphael Berthier, Andrea Montanari, and Phan-Minh Nguyen · 2017
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Consistent parameter estimation for lasso and approximate message passing
Ali Mousavi, Arian Maleki, and Richard G Baraniuk · 2017
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A universal analysis of large-scale regularized least squares solutions
Ashkan Panahi and Babak Hassibi · 2017
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Optimal errors and phase transitions in high-dimensional generalized linear models
Jean Barbier, Florent Krzakala, Nicolas Macris, Léo Miolane, and Lenka Zdeborová · 2018
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On the impact of predictor geometry on the performance on high-dimensional ridge-regularized generalized robust regression estimators
Noureddine El Karoui · 2018
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Junjie Ma, Ji Xu, and Arian Maleki · 2018
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A modern maximum-likelihood theory for high-dimensional logistic regression
Pragya Sur and Emmanuel J Candès · 2018
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Takashi Takahashi and Yoshiyuki Kabashima · 2018
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Precise error analysis of regularized m-estimators in high-dimensions
Christos Thrampoulidis, Ehsan Abbasi, and Babak Hassibi · 2018
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