Fetching the paper…
Reading the bibliography…
The OSCAR (octagonal selection and clustering algorithm for regression) regularizer consists of a L_1 norm plus a pair-wise L_inf norm (responsible for its grouping behavior) and was proposed to encourage group sparsity in scenarios where the groups are a priori unknown.
R. Courant, “Variational methods for the solution of problems of equilibrium and vibrations,” Bull. Amer. Math. Soc , vol. 49, p. 23, 1943
1943
Earlier work this paper cites.
J. Moreau, “Fonctions convexes duales et points proximaux dans un espace hilbertien,” CR Acad. Sci. Paris Sér. A Math , vol. 255, pp. 2897–2899, 1962
1962
Earlier work this paper cites.
——, “A method of solving a convex programming problem with convergence rate 𝒪 ( 1 / k 2 ) \mathcal{O}(1/k^{2}) ,” in Soviet Mathematics Doklady , vol. 27, 1983, pp. 372–376
1983
Earlier work this paper cites.
J. Barzilai and J. Borwein, “Two-point step size gradient methods,” IMA Journal of Numerical Analysis , vol. 8, pp. 141–148, 1988
1988
Earlier work this paper cites.
J. Eckstein and D. Bertsekas, “On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators,” Mathematical Programming , vol. 5, pp. 293–318, 1992
1992
Earlier work this paper cites.
B. Natarajan, “Sparse approximate solutions to linear systems,” SIAM journal on computing , vol. 24, pp. 227–234, 1995
1995
Earlier work this paper cites.
R. Tibshirani, “Regression shrinkage and selection via the lasso,” Journal of the Royal Statistical Society (B) , pp. 267–288, 1996
1996
Earlier work this paper cites.
M. Osborne, B. Presnell, and B. Turlach, “On the lasso and its dual,” Journal of Computational and Graphical statistics , vol. 9, pp. 319–337, 2000
2000
Earlier work this paper cites.
M. Figueiredo and R. Nowak, “An EM algorithm for wavelet-based image restoration,” IEEE Transactions on Image Processing , vol. 12, pp. 906–916, 2003
2003
Earlier work this paper cites.
I. Daubechies, M. Defrise, and C. De Mol, “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Communications on pure and applied mathematics , vol. 57, pp. 1413–1457, 2004
2004
Earlier work this paper cites.
B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani, “Least angle regression,” The Annals of statistics , vol. 32, pp. 407–499, 2004
2004
Earlier work this paper cites.
Y. Nesterov, “Introductory lectures on convex optimization, 2004.”
2004
Earlier work this paper cites.
R. Tibshirani, M. Saunders, S. Rosset, J. Zhu, and K. Knight, “Sparsity and smoothness via the fused lasso,” Journal of the Royal Statistical Society (B) , vol. 67, pp. 91–108, 2004
2004
Earlier work this paper cites.
E. Candes and T. Tao, “Decoding by linear programming,” IEEE Transactions on Information Theory , vol. 51, pp. 4203–4215, 2005
2005
Earlier work this paper cites.
P. Combettes and V. Wajs, “Signal recovery by proximal forward-backward splitting,” Multiscale Modeling & Simulation , vol. 4, pp. 1168–1200, 2005
2005
Earlier work this paper cites.
——, “A bound optimization approach to wavelet-based image deconvolution,” in IEEE International Conference on Image Processing , 2005, pp. II.782–II.785
2005
Earlier work this paper cites.
M. Yuan and Y. Lin, “Model selection and estimation in regression with grouped variables,” Journal of the Royal Statistical Society (B) , vol. 68, pp. 49–67, 2005
2005
Earlier work this paper cites.
2005
Earlier work this paper cites.
E. Candès, “Compressive sampling,” in Proceedings oh the International Congress of Mathematicians: Madrid, August 22-30, 2006: invited lectures , 2006, pp. 1433–1452
2006
Earlier work this paper cites.
E. Candes, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Communications on Pure and Applied Mathematics , vol. 59, pp. 1207–1223, 2006
2006
Earlier work this paper cites.
D. L. Donoho, “Compressed sensing,” IEEE Transactions on Information Theory , vol. 52, pp. 1289–1306, 2006
2006
Earlier work this paper cites.
D. Donoho, I. Drori, Y. Tsaig, and J. Starck, Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit , 2006
2006
Earlier work this paper cites.
H. Zou, “The adaptive lasso and its oracle properties,” Journal of the American Statistical Association , vol. 101, pp. 1418–1429, 2006
2006
Cited alongside, same era.
J. Bioucas-Dias and M. Figueiredo, “A new twist: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Transactions on Image Processing , vol. 16, pp. 2992–3004, 2007
2007
Cited alongside, same era.
H. Bondell and B. Reich, “Simultaneous regression shrinkage, variable selection, and supervised clustering of predictors with OSCAR,” Biometrics , vol. 64, pp. 115–123, 2007
2007
Cited alongside, same era.
R. Chartrand, “Exact reconstructions of sparse signals via nonconvex minimization,” IEEE Signal Processing Letters , vol. 14, pp. 707–710, 2007
2007
Cited alongside, same era.
M. Elad, Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing . Springer, 2010
2010
Later among the works it cites.
A. Langer and M. Fornasier, “Analysis of the adaptive iterative bregman algorithm,” preprint , vol. 3, 2010
2010
Later among the works it cites.
J. Liu and J. Ye, “Fast overlapping group lasso,” arXiv preprint arXiv:1009.0306 , 2010
2010
Later among the works it cites.
2010
Later among the works it cites.
C. Micchelli, J. Morales, and M. Pontil, “Regularizers for structured sparsity,” Advances in Computational Mathematics , pp. 1–35, 2010
2010
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2007
Cited alongside, same era.
E. Hale, W. Yin, and Y. Zhang, “A fixed-point continuation method for l1-regularized minimization with applications to compressed sensing,” CAAM TR07-07, Rice University , 2007
2007
Cited alongside, same era.
Y. Tsaig, “Sparse solution of underdetermined linear systems: algorithms and applications,” Ph.D. dissertation, Stanford University, 2007
2007
Cited alongside, same era.
E. Candes, M. Wakin, and S. Boyd, “Enhancing sparsity by reweighted ℓ 1 \ell_{1} minimization,” Journal of Fourier Analysis and Applications , vol. 14, pp. 877–905, 2008
2008
Cited alongside, same era.
R. Chartrand and W. Yin, “Iteratively reweighted algorithms for compressive sensing,” in IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) , 2008, pp. 3869–3872
2008
Cited alongside, same era.
Y. Wang, J. Yang, W. Yin, and Y. Zhang, “A new alternating minimization algorithm for total variation image reconstruction,” SIAM Journal on Imaging Sciences , vol. 1, pp. 248–272, 2008
2008
Cited alongside, same era.
W. Yin, S. Osher, D. Goldfarb, and J. Darbon, “Bregman iterative algorithms for ℓ 1 \ell_{1} -minimization with applications to compressed sensing,” SIAM Journal on Imaging Sciences , vol. 1, pp. 143–168, 2008
2008
Cited alongside, same era.
A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM Journal on Imaging Sciences , vol. 2, pp. 183–202, 2009
2009
Cited alongside, same era.
Later among the works it cites.
S. Petry, C. Flexeder, and G. Tutz, “Pairwise fused lasso,” Technical Report 102, Department of Statistics LMU Munich , 2010
2010
Later among the works it cites.
S. Setzer, G. Steidl, and T. Teuber, “Deblurring poissonian images by split Bregman techniques,” Journal of Visual Communication and Image Representation , vol. 21, pp. 193–199, 2010
2010
Later among the works it cites.
X. Shen and H. Huang, “Grouping pursuit through a regularization solution surface,” Journal of the American Statistical Association , vol. 105, pp. 727–739, 2010
2010
Later among the works it cites.
D. Wipf and S. Nagarajan, “Iterative reweighted l1 and l2 methods for finding sparse solutions,” IEEE Journal of Selected Topics in Signal Processing , vol. 4, pp. 317–329, 2010
2010
Later among the works it cites.
——, “An augmented lagrangian approach to the constrained optimization formulation of imaging inverse problems,” IEEE Transactions on Image Processing , vol. 20, pp. 681–695, 2011
2011
Later among the works it cites.
S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Foundations and Trends® in Machine Learning , vol. 3, pp. 1–122, 2011
2011
Later among the works it cites.
A. Chambolle and T. Pock, “A first-order primal-dual algorithm for convex problems with applications to imaging,” Journal of Mathematical Imaging and Vision , vol. 40, pp. 120–145, 2011
2011
Later among the works it cites.
J. Huang, T. Zhang, and D. Metaxas, “Learning with structured sparsity,” The Journal of Machine Learning Research , vol. 999888, pp. 3371–3412, 2011
2011
Later among the works it cites.
2011
Later among the works it cites.
S. Petry and G. Tutz, “The oscar for generalized linear models,” Technical Report 112, Department of Statistics LMU Munich , 2011
2011
Later among the works it cites.
F. Bach, R. Jenatton, J. Mairal, and G. Obozinski, “Structured sparsity through convex optimization,” Statistical Science , vol. 27, pp. 450–468, 2012
2012
Later among the works it cites.
Z. Qin and D. Goldfarb, “Structured sparsity via alternating direction methods,” The Journal of Machine Learning Research , vol. 98888, pp. 1435–1468, 2012
2012
Later among the works it cites.
N. Simon, J. Friedman, T. Hastie, and R. Tibshirani, “The sparse-group lasso,” Journal of Computational and Graphical Statistics , 2012, to appear
2012
Later among the works it cites.
S. Yang, L. Yuan, Y.-C. Lai, X. Shen, P. Wonka, and J. Ye, “Feature grouping and selection over an undirected graph,” in Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining . ACM, 2012, pp. 922–930
2012
Later among the works it cites.
H. Zhang, L. Cheng, and J. Li, “Reweighted minimization model for mr image reconstruction with split Bregman method,” Science China Information sciences , pp. 1–10, 2012
2012
Later among the works it cites.
L. Zhong and J. Kwok, “Efficient sparse modeling with automatic feature grouping,” IEEE Transactions on Neural Networks and Learning Systems , vol. 23, pp. 1436–1447, 2012
2012
Later among the works it cites.