Regularization paths for generalized linear models via coordinate descent

Regularization paths for generalized linear models via coordinate descent (2009)

Cached

Download Links

by Jerome Friedman , Trevor Hastie , Rob Tibshirani

Citations:

BibTeX

@MISC{Friedman09regularizationpaths,
    author = {Jerome Friedman and Trevor Hastie and Rob Tibshirani},
    title = {Regularization paths for generalized linear models via coordinate descent },
    year = {2009}
}

Bookmark

OpenURL

Abstract

We develop fast algorithms for estimation of generalized linear models with convex penalties. The models include linear regression, twoclass logistic regression, and multinomial regression problems while the penalties include ℓ1 (the lasso), ℓ2 (ridge regression) and mixtures of the two (the elastic net). The algorithms use cyclical coordinate descent, computed along a regularization path. The methods can handle large problems and can also deal efficiently with sparse features. In comparative timings we find that the new algorithms are considerably faster than competing methods.

Citations

1089	Atomic decomposition by basis pursuit - Chen, Donoho, et al. - 1998
998	Regression shrinkage and selection via the lasso - Tibshirani - 1996
812	Molecular classification of cancer: class discovery and class prediction by gene expression monitoring - Golub, Slonim, et al. - 1999
578	Ideal spatial adaptation by wavelet shrinkage - Donoho - 1994
478	Least angle regression - Efron - 2004
353	Newsweeder: Learning to filter netnews - Lang - 1995
238	Y: Model selection and estimation in regression with grouped variables - Yuan, Lin
236	An iterative thresholding algorithm for linear inverse problems with a sparsity constraint - Daubechies, Defrise, et al. - 2004
228	The Dantzig selector: statistical estimation when p is much larger than n - Candès, Tao - 2007
173	Variable selection via nonconcave penalized likelihood and its oracle properties - Fan, Li
160	Multiclass cancer diagnosis using tumor gene expression signatures - Ramaswamy, Tamayo, et al. - 2001
159	Regularization and Variable Selection via the Elastic Net - Zou, Hastie - 2008
121	A new approach to variable selection in least squares problems - Osborne, Presnell, et al. - 2000
118	The Adaptive Lasso and Its Oracle Properties - Zou - 2006
114	Sparse inverse covariance estimation with the graphical lasso.” Biostatistics - Friedman, Hastie, et al. - 2008
107	The entire regularization path for the support vector machine - Hastie, Rosset, et al. - 2004
96	Core Team (2009). R: A language and environment for statistical computing. R Foundation for Statistical Computing - Development
92	Pathwise coordinate optimization - Friedman, Hastie, et al.
79	Buhlmann P: Boosting for tumor classification with gene expression data - Dettling
77	An interior-point method for large-scale l1regularized logistic regression - Koh, SJ, et al. - 2007
75	The group lasso for logistic regression - Meier, Geer, et al. - 2008
74	Large-scale Bayesian logistic regression for text categorization - Genkin, Lewis, et al. - 2007
67	Sparse multinomial logistic regression: fast algorithms and generalization bounds - Krishnapuram, Carin, et al. - 2005
62	Scalable training of L1-regularized log-linear models - Andrew, Gao
57	Convergence of a block coordinate descent method for nondifferentiable minimization - Tseng - 2001
55	Gaasenbeek M, Mesirov JP, Coller H, Loh ML, Downing JR, Caligiuri MA, et al.: Molecular classification of cancer: class discovery and class prediction by gene expression monitoring - TR, DK, et al. - 1999
53	Piecewise linear regularized solution paths - Rosset, Zhu - 2003
42	Learning to remove internet advertisements - Kushmerick - 1999
42	A simple and efficient algorithm for gene selection using sparse logistic regression - Shevade, Keerthi
36	T: Classification of gene microarrays by penalized logistic regression - Zhu, Hastie
35	The Lasso method for variable selection - Tibshirani - 1997
33	Regularization and variable selection via the elastic - Zou, Hastie - 2005
30	Coordinate descent algorithms for lasso penalized regression - WU, K - 2008
28	L1 regularization path algorithm for generalized linear models - Park, Hastie - 2007
22	An L1 regularization-path algorithm for generalized linear models - Park, Hastie - 2006
15	Tibshirani R - Hastie - 1990
15	L1-Regularization Path Algorithm for Generalized Linear Models - MY, Hastie
12	Fast sparse regression and classification - FRIEDMAN
10	Defrise M, De Mol C (2004) An iterative thresholding algorithm for linear inverse problems with a sparsity constraint - Daubechies
9	Penalized Regressions: the Bridge vs the Lasso - Fu - 1998
8	Coordinate descent procedures for lasso penalized regression - Wu, Lange - 2008
4	Adaptable, efficient and robust methods for regression and classification via piecewise linear regularized coefficient paths - Rosset, Zhu - 2003
4	Atomic decomposition by basis pursuit - SS, DL, et al. - 1999
4	2006a) glmpath: L1 Regularization Path for Generalized Linear Models and Proportional Hazards Model. URL http://cran.r-project.org/src/contrib/Descriptions/glmpath.html. R package version 0.91 - Park, Hastie
2	The Elements of Statistical Learning: Prediction, Inference and Data Mining. 2nd edition - Hastie, Tibshirani, et al. - 2009
2	2005a) elasticnet: Elastic Net Regularization and Variable Selection. R package version - Zou, Hastie
2	Prediction accuracy and stability of regrsssion with optimal sclaing transformations - Kooij - 2007
1	Efficient l1 logistic regression - Lee, Lee, et al. - 2006
1	der Kooij. Prediction accuracy and stability of regrsssion with optimal sclaing transformations - Van - 2007
1	Genome-Wide Association Analysis by Penalized Logistic Regression - Wu, Chen, et al. - 2009