The predictive Lasso
We propose a shrinkage procedure for simultaneous variable selection and estimation in generalized linear models (GLMs) with an explicit predictive motivation. The procedure estimates the coefficients by minimizing the Kullback-Leibler divergence of a set of predictive distributions to the correspon...
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| Published in | Statistics and computing Vol. 22; no. 5; pp. 1069 - 1084 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Boston
Springer US
01.09.2012
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0960-3174 1573-1375 |
| DOI | 10.1007/s11222-011-9279-3 |
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| Abstract | We propose a shrinkage procedure for simultaneous variable selection and estimation in generalized linear models (GLMs) with an explicit predictive motivation. The procedure estimates the coefficients by minimizing the Kullback-Leibler divergence of a set of predictive distributions to the corresponding predictive distributions for the full model, subject to an
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constraint on the coefficient vector. This results in selection of a parsimonious model with similar predictive performance to the full model. Thanks to its similar form to the original Lasso problem for GLMs, our procedure can benefit from available
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1
-regularization path algorithms. Simulation studies and real data examples confirm the efficiency of our method in terms of predictive performance on future observations. |
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| AbstractList | We propose a shrinkage procedure for simultaneous variable selection and estimation in generalized linear models (GLMs) with an explicit predictive motivation. The procedure estimates the coefficients by minimizing the Kullback-Leibler divergence of a set of predictive distributions to the corresponding predictive distributions for the full model, subject to an
l
1
constraint on the coefficient vector. This results in selection of a parsimonious model with similar predictive performance to the full model. Thanks to its similar form to the original Lasso problem for GLMs, our procedure can benefit from available
l
1
-regularization path algorithms. Simulation studies and real data examples confirm the efficiency of our method in terms of predictive performance on future observations. |
| Author | Tran, Minh-Ngoc Leng, Chenlei Nott, David J. |
| Author_xml | – sequence: 1 givenname: Minh-Ngoc surname: Tran fullname: Tran, Minh-Ngoc email: ngoctm@nus.edu.sg, minh-ngoc.tran@unsw.edu.au organization: Department of Statistics and Applied Probability, National University of Singapore, Australian School of Business, University of New South Wales – sequence: 2 givenname: David J. surname: Nott fullname: Nott, David J. organization: Department of Statistics and Applied Probability, National University of Singapore – sequence: 3 givenname: Chenlei surname: Leng fullname: Leng, Chenlei organization: Department of Statistics and Applied Probability, National University of Singapore |
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| Cites_doi | 10.1198/016214508000000337 10.1080/03610920903486798 10.1093/biomet/62.3.547 10.1016/S0378-3758(02)00286-0 10.1214/ss/1009212519 10.1111/j.1467-9868.2005.00503.x 10.1016/j.csda.2010.01.036 10.1198/016214506000001437 10.1214/08-AOAS191 10.1198/016214506000000735 10.1111/1467-9868.00348 10.1175/1520-0434(2000)015<0559:DOTCRP>2.0.CO;2 10.1111/j.2517-6161.1968.tb01505.x 10.1080/01621459.1997.10473615 10.1007/978-1-4899-4467-2 10.5296/jse.v4i1.4306 10.1111/j.2517-6161.1996.tb02080.x 10.1111/j.2517-6161.1952.tb00104.x |
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| Keywords | Kullback-Leibler divergence Optimal prediction Lasso Generalized linear models Variable selection |
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| References | Johnson (CR14) 1996; 4 Chen, Ibrahim (CR5) 2003; 13 Aitchison (CR1) 1975; 62 Zellner (CR24) 1986 CR15 Hoeting, Madigan, Raftery, Volinsky (CR13) 1999; 14 Geisser (CR7) 1980; 143 Good (CR11) 1952; 14 Park, Casella (CR19) 2008; 103 Dupuis, Robert (CR6) 2003; 111 Bailey (CR2) 1994 O’Hagan, Forster (CR18) 2004 Geisser (CR8) 1993 Tibshirani (CR21) 1996; 58 Raftery, Madigan, Hoeting (CR20) 1997; 92 Gneiting, Raftery (CR10) 2007; 102 Hersbach (CR12) 2000; 15 Nott, Leng (CR17) 2010; 54 Lindley (CR16) 1968; 30 CR23 Zhao, Yu (CR25) 2006; 7 Burnham, Anderson (CR4) 2002 Zou (CR26) 2006; 101 Brown, Vannucci, Fearn (CR3) 2002; 64 Gelman, Jakulin, Grazia, Su (CR9) 2008; 2 Tran (CR22) 2011; 40 Zou, Hastie (CR27) 2005; 67 A. Zellner (9279_CR24) 1986 R. Tibshirani (9279_CR21) 1996; 58 H. Zou (9279_CR27) 2005; 67 H. Hersbach (9279_CR12) 2000; 15 A. O’Hagan (9279_CR18) 2004 I.J. Good (9279_CR11) 1952; 14 S. Geisser (9279_CR8) 1993 P. Zhao (9279_CR25) 2006; 7 J. Aitchison (9279_CR1) 1975; 62 H. Zou (9279_CR26) 2006; 101 9279_CR15 D.J. Nott (9279_CR17) 2010; 54 C. Bailey (9279_CR2) 1994 T. Park (9279_CR19) 2008; 103 R.W. Johnson (9279_CR14) 1996; 4 K.P. Burnham (9279_CR4) 2002 D.V. Lindley (9279_CR16) 1968; 30 M.H. Chen (9279_CR5) 2003; 13 J.A. Dupuis (9279_CR6) 2003; 111 A. Gelman (9279_CR9) 2008; 2 J.A. Hoeting (9279_CR13) 1999; 14 S. Geisser (9279_CR7) 1980; 143 T. Gneiting (9279_CR10) 2007; 102 A.E. Raftery (9279_CR20) 1997; 92 M.N. Tran (9279_CR22) 2011; 40 9279_CR23 P.J. Brown (9279_CR3) 2002; 64 |
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| Title | The predictive Lasso |
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