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SLOPE is a relatively new convex optimization procedure for high-dimensional linear regression via the sorted l1 penalty: the larger the rank of the fitted coefficient, the larger the penalty.
Stochastic processes
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Principles of mathematical analysis
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Real analysis
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Diameters of some finite-dimensional sets and classes of smooth functions
B. S. Kashin · 1977
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The theory of error-correcting codes
F. J. MacWilliams and N. J. A. Sloane · 1977
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Positively correlated normal variables are associated
L. D. Pitt · 1982
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Regression shrinkage and selection via the lasso
R. Tibshirani · 1996
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Nonlinear wavelet image processing: variational problems, compression, and noise removal through wavelet shrinkage
A. Chambolle, R. A. De Vore, N.-Y. Lee, and B. J. Lucier · 1998
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The concentration of measure phenomenon
M. Ledoux · 2001
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An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
I. Daubechies, M. Defrise, and C. De Mol · 2004
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Smallest singular value of random matrices and geometry of random polytopes
A. E. Litvak, A. Pajor, M. Rudelson, and N. Tomczak-Jaegermann · 2005
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Limit of the smallest eigenvalue of a large dimensional sample covariance matrix
Z. Bai and Y. Yin · 2008
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Simultaneous regression shrinkage, variable selection, and supervised clustering of predictors with oscar
H. D. Bondell and B. J. Reich · 2008
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A fast iterative shrinkage-thresholding algorithm for linear inverse problems
A. Beck and M. Teboulle · 2009
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Message-passing algorithms for compressed sensing
D. L. Donoho, A. Maleki, and A. Montanari · 2009
Cited alongside, same era.
Variational analysis
R. T. Rockafellar and R. J.-B. Wets · 2009
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The dynamics of message passing on dense graphs, with applications to compressed sensing
M. Bayati and A. Montanari · 2011
Cited alongside, same era.
The lasso risk for gaussian matrices
M. Bayati and A. Montanari · 2011
Cited alongside, same era.
The noise-sensitivity phase transition in compressed sensing
D. L. Donoho, A. Maleki, and A. Montanari · 2011
Cited alongside, same era.
Controlling the false discovery rate via knockoffs
R. F. Barber and E. J. Candès · 2015
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SLOPE—adaptive variable selection via convex optimization
M. Bogdan, E. Van Den Berg, C. Sabatti, W. Su, and E. J. Candès · 2015
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High dimensional robust m-estimation: Asymptotic variance via approximate message passing
D. Donoho and A. Montanari · 2016
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Ordered weighted l1 regularized regression with strongly correlated covariates: Theoretical aspects
M. Figueiredo and R. Nowak · 2016
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SLOPE is adaptive to unknown sparsity and asymptotically minimax
W. Su and E. Candès · 2016
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State evolution for approximate message passing with non-separable functions
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Generalized approximate message passing for estimation with random linear mixing
S. Rangan · 2011
Cited alongside, same era.
Probabilistic reconstruction in compressed sensing: algorithms, phase diagrams, and threshold achieving matrices
F. Krzakala, M. Mézard, F. Sausset, Y. Sun, and L. Zdeborová · 2012
Cited alongside, same era.
Graphical models concepts in compressed sensing
A. Montanari · 2012
Cited alongside, same era.
Estimating lasso risk and noise level
M. Bayati, M. A. Erdogdu, and A. Montanari · 2013
Cited alongside, same era.
State evolution for general approximate message passing algorithms, with applications to spatial coupling
A. Javanmard and A. Montanari · 2013
Cited alongside, same era.
Proximal algorithms
N. Parikh, S. Boyd, et al · 2014
Cited alongside, same era.
R. Berthier, A. Montanari, and P.-M. Nguyen · 2017
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False discoveries occur early on the lasso path
W. Su, M. Bogdan, and E. Candès · 2017
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SLOPE meets lasso: improved oracle bounds and optimality
P. C. Bellec, G. Lecué, and A. B. Tsybakov · 2018
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Group SLOPE—adaptive selection of groups of predictors
D. Brzyski, A. Gossmann, W. Su, and M. Bogdan · 2018
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Consistent parameter estimation for lasso and approximate message passing
A. Mousavi, A. Maleki, R. G. Baraniuk, et al · 2018
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Finite sample analysis of approximate message passing algorithms
C. Rush and R. Venkataramanan · 2018
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Fundamental barriers to high-dimensional regression with convex penalties
M. Celentano and A. Montanari · 2019
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Asymptotics and optimal designs of SLOPE for sparse linear regression
H. Hu and Y. M. Lu · 2019
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