Fetching the paper…
Reading the bibliography…
We consider a sparse high dimensional regression model where the goal is to recover a $k$-sparse unknown vector $\beta^*$ from $n$ noisy linear observations of the form $Y=X\beta^*+W \in \mathbb{R}^n$ where $X \in \mathbb{R}^{n \times p}$ has iid $N(0,1)$ entries and $W \in \mathbb{R}^n$ has iid $N(0,\sigma^2)$ entries.
A bound on tail probabilities for quadratic forms in independent random variables
D. L. Hanson and F. T. Wright · 1971
Earlier work this paper cites.
Model selection via multifold cross validation
Ping Zhang · 1993
Earlier work this paper cites.
Atomic decomposition by basis pursuit
Scott Shaobing Chen, David L. Donoho, and Michael A. Saunders · 2001
Earlier work this paper cites.
Decoding by linear programming
Emmanuel J Candes and Terence Tao · 2005
Earlier work this paper cites.
Stable signal recovery from incomplete and inaccurate measurements
Emmanuel J. Candes, Justin K. Romberg, and Terence Tao · 2006
Earlier work this paper cites.
Compressed sensing
David L Donoho · 2006
Earlier work this paper cites.
High-dimensional graphs and variable selection with the lasso
Nicolai Meinshausen and Peter Bühlmann · 2006
Earlier work this paper cites.
The dantzig selector: Statistical estimation when p is much larger than n
Emmanuel Candes and Terence Tao · 2007
Earlier work this paper cites.
Algorithmic barriers from phase transitions
Dimitris Achlioptas and Amin Coja-Oghlan · 2008
Earlier work this paper cites.
A simple proof of the restricted isometry property for random matrices
Richard Baraniuk, Mark Davenport, Ronald DeVore, and Michael Wakin · 2008
Earlier work this paper cites.
High-dimensional sparse factor modeling: Applications in gene expression genomics
Carlos M. Carvalho, Jeffrey Chang, Joseph E. Lucas, Joseph R. Nevins, Quanli Wang, and Mike West · 2008
Earlier work this paper cites.
Compressed sensing mri
M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly · 2008
Earlier work this paper cites.
An overview of recent developments in genomics and associated statistical methods
Peter J. Bickel, James B. Brown, Haiyan Huang, and Qunhua Li · 2009
Earlier work this paper cites.
Simultaneous analysis of lasso and dantzig selector
Peter J. Bickel, Ya’acov Ritov, and Alexandre B. Tsybakov · 2009
Earlier work this paper cites.
Iterative hard thresholding for compressed sensing
Thomas Blumensath and Mike E. Davies · 2009
Earlier work this paper cites.
On consistency and sparsity for principal components analysis in high dimensions
Iain M Johnstone and Arthur Yu Lu · 2009
Earlier work this paper cites.
On the conditions used to prove oracle results for the lasso
Sara A. van de Geer and Peter Bühlmann · 2009
Cited alongside, same era.
Information-theoretic limits on sparsity recovery in the high-dimensional and noisy setting
Martin J Wainwright · 2009
Cited alongside, same era.
Sharp thresholds for high-dimensional and noisy sparsity recovery using constrained quadratic programming (lasso)
Martin J Wainwright · 2009
Cited alongside, same era.
Counting the faces of randomly-projected hypercubes and orthants, with applications
David L. Donoho and Jared Tanner · 2010
Cited alongside, same era.
Information-theoretic limits on sparse signal recovery: Dense versus sparse measurement matrices
Wei Wang, Martin J Wainwright, and Kannan Ramchandran · 2010
Cited alongside, same era.
On the solution space geometry of random formulas
The squared-error of generalized lasso: A precise analysis
S. Oymak, C. Thrampoulidis, and B. Hassibi · 2013
Later among the works it cites.
Approximate sparsity pattern recovery: Information-theoretic lower bounds
Galen Reeves and Michael Gapstar · 2013
Later among the works it cites.
Replica analysis and approximate message passing decoder for superposition codes
J. Barbier and F. Krzakala · 2014
Later among the works it cites.
Accelerated mr parameter mapping with low‐rank and sparsity constraints
Zhao Bo, Wenmiao Lu, T. Kevin Hitchens, Fan Lam, Chien Ho, and Zhi‐Pei Liang · 2014
Later among the works it cites.
Fast sparse superposition codes have near exponential error probability for r < ⌋ r<{\cal c}
A. Joseph and A. R. Barron · 2014
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
D. Achlioptas, A. Coja-Oghlan, and F. Ricci-Tersenghi · 2011
Cited alongside, same era.
Orthogonal matching pursuit for sparse signal recovery with noise
T. T. Cai and L. Wang · 2011
Cited alongside, same era.
On independent sets in random graphs
A. Coja-Oghlan and C. Efthymiou · 2011
Cited alongside, same era.
Global testing under sparse alternatives: Anova, multiple comparisons and the higher criticism
Emmanuel J. Cand‘es Ery Arias-Castro and Yaniv Plan · 2011
Cited alongside, same era.
Reconstruction and clustering in random constraint satisfaction problems
Andrea Montanari, Ricardo Restrepo, and Prasad Tetali · 2011
Cited alongside, same era.
Nearly sharp sufficient conditions on exact sparsity pattern recovery
K. Rahnama Rad · 2011
Cited alongside, same era.
The variable selection problem
Edward I. George · 2012
Cited alongside, same era.
Mustazee Rahman and Balint Virag · 2014
Later among the works it cites.
Statistical Learning with Sparsity: The Lasso and Generalizations
Trevor Hastie, Robert Tibshirani, and Martin J. Wainwright · 2015
Later among the works it cites.
Finding a large submatrix of a gaussian random matrix
David Gamarnik and Quan Li · 2016
Later among the works it cites.
Consensus-based sparse signal reconstruction algorithm for wireless sensor networks
Bao Peng, Zhi Zhao, Guangjie Han, and Jian Shen · 2016
Later among the works it cites.
The box-lasso with application to gssk modulation in massive mimo systems
I. Ben Atitallah, C. Thrampoulidis, A. Kammoun, T. Y. Al-Naffouri, M. Alouini, and B. Hassibi · 2017
Closest in time.
Sparse high dimensional regression: Exact scalable algorithms and phase transitions
D. Bertsimas and Bart Van Parys · 2017
Closest in time.
High dimensional linear regression with binary coefficients: Mean squared error and a phase transition
David Gamarnik and Ilias Zadik · 2017
Closest in time.
Eigenprism: inference for high dimensional signal-to-noise ratios
Lucas Janson, Rina Foygel Barber, and Emmanuel Candès · 2017
Closest in time.
Capacity-achieving sparse superposition codes via approximate message passing decoding
C. Rush, A. Greig, and R. Venkataramanan · 2017
Closest in time.
Accuracy assessment for high-dimensional linear regression1
T. Tony Cai and Zijian Gao · 2018
Closest in time.