The DOI matches its Crossref record; 18 of the 18 references it cites were found in a registry or an index.
Pathwise coordinate optimization
Open accessAbstract
We consider “one-at-a-time” coordinate-wise descent algorithms for a class of convex optimization problems. An algorithm of this kind has been proposed for the L1-penalized regression (lasso) in the literature, but it seems to have been largely ignored. Indeed, it seems that coordinate-wise algorithms are not often used in convex optimization. We show that this algorithm is very competitive with the well-known LARS (or homotopy) procedure in large lasso problems, and that it can be applied to related methods such as the garotte and elastic net. It turns out that coordinate-wise descent does not work in the “fused lasso,” however, so we derive a generalized algorithm that yields the solution in much less time that a standard convex optimizer. Finally, we generalize the procedure to the two-dimensional fused lasso, and demonstrate its performance on some image smoothing problems.
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Regression shrinkage and selection via the lasso
Tibshirani, R. (1996) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1996.tb02080.x · Cited by 51,482
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Zou, H., & Hastie, T. (2005) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2005.00503.x · Cited by 20,957
Self-citationNonlinear total variation based noise removal algorithms
Rudin, L. I., Osher, S., & Fatemi, E. (1992) · Physica D: Nonlinear Phenomena · doi:10.1016/0167-2789(92)90242-f · Cited by 15,704
Bertsekas, D. P. (1997) · Journal of the Operational Research Society · doi:10.1038/sj.jors.2600425 · Cited by 11,726
Efron, B., Hastie, T., Johnstone, I., & Tibshirani, R. (2004) · The Annals of Statistics · doi:10.1214/009053604000000067 · Cited by 9,357
Self-citationModel Selection and Estimation in Regression with Grouped Variables
Yuan, M., & Lin, Y. (2006) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2005.00532.x · Cited by 7,261
Atomic Decomposition by Basis Pursuit
Chen, S. S., Donoho, D. L., & Saunders, M. A. (1998) · SIAM Journal on Scientific Computing · doi:10.1137/s1064827596304010 · Cited by 6,845
An iterative thresholding algorithm for linear inverse problems with a sparsity constraint.
Daubechies, I., Defrise, M., & De Mol, C. (2004) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.20042 · Cited by 4,958
Adapting to Unknown Smoothness via Wavelet Shrinkage
Donoho, D. L., & Johnstone, I. M. (1995) · Journal of the American Statistical Association · doi:10.1080/01621459.1995.10476626 · Cited by 4,630
Sparsity and Smoothness Via the Fused Lasso
Tibshirani, R., Saunders, M., Rosset, S., Zhu, J., & Knight, K. (2005) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2005.00490.x · Cited by 2,724
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Chang, C. C., Chow, C. C., Tellier, L. C., Vattikuti, S., Purcell, S. M., & Lee, J. J. (2015) · Gigascience · doi:10.1186/s13742-015-0047-8 · Cited by 12,709
Sparse inverse covariance estimation with the graphical lasso
Friedman, J., Hastie, T., & Tibshirani, R. (2008) · Biostatistics · doi:10.1093/biostatistics/kxm045 · Cited by 6,355
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Fan, J., & Lv, J. (2008) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2008.00674.x · Cited by 2,711
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Guo, Y., Liu, Y., Oerlemans, A., Lao, S., Wu, S., & Lew, M. S. (2016) · Neurocomputing · doi:10.1016/j.neucom.2015.09.116 · Cited by 2,504
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Metadata
- Authors
- Friedman, J., Hastie, T., Höfling, H., & Tibshirani, R.
- Venue
- The Annals of Applied Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 2007-12-01
- Volume
- 1
- Issue
- 2
- Pages
- 302-332
- ISSN
- 1932-6157 (ISSN-L)
- OpenAlex
- W2056636001
- Cited by
- 1,895
- References
- 18
- FWCI
- 51.65
- Type
- journal article
- Language
- en
- Open access
- bronze
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