Parsimonious additive models

Computational Statistics and Data Analysis

Volumn 51, Issue 6, 2007, Pages 2851-2870

  Avalos, Marta ^a,b   Grandvalet, Yves ^a   Ambroise, Christophe ^a  

^a UNIVERSITÉ DE TECHNOLOGIE DE COMPIÈGNE   (France)

^b INSERM   (France)

Author keywords

Function estimation; Interpretable models; Lasso; Model selection; Nonparametric regression; Penalization; Smoothing; Splines; Supervised learning; Variable selection

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; DATA REDUCTION; LEARNING SYSTEMS; LINEAR SYSTEMS; NONLINEAR SYSTEMS; PARAMETER ESTIMATION; REGRESSION ANALYSIS;

FUNCTION ESTIMATION; INTERPRETABLE MODELS; MODEL SELECTION; NONPARAMETRIC REGRESSION; SUPERVISED LEARNING;

FUNCTION EVALUATION;

EID: 33846588964     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2006.10.007     Document Type: Article

References (40)

1. Avalos M., Grandvalet Y., and Ambroise C. Regularization methods for additive models. In: Berthold M.R., Lenz H.J., Bradley E., Kruse R., and Borgelt C. (Eds). Fifth International Symposium on Intelligent Data Analysis, Lecture Notes Computer Science (2003), Springer, Berlin 509-520
2. Bacchetti P., and Quale C. Generalized additive models with interval-censored data and time-varying covariates: application to human immunodeficiency virus infection in hemophiliacs. Biometrics 58 2 (2002) 443-447
3. Bakin, S., 1999. Adaptive regression and model selection in data mining problems. Ph.D. Thesis, School of Mathematical Sciences, The Australian National University, Canberra.
4. Beck N., and Jackman S. Beyond linearity by default: generalized additive models. Amer. J. Political Sci. 42 (1998) 596-627
5. Breiman L. Heuristics of instability and stabilization in model selection. Ann. Statist. 24 6 (1996) 2350-2383
6. Brendel, K., Legrand, M., Taburet, A.M., Baron, G., Goujard, C., Mentre, F., Cophar 1-ANRS 102 Trial Group, 2005. Population pharmacokinetic analysis of indinavir in HIV-infected patient treated with a stable antiretroviral therapy. Fund. Clin. Pharmacol. 19(3), 373-383.
7. Brumback B.A., Ruppert D., and Wand M.P. Comment on "Variable selection and function estimation in additive nonparametric regression using a data-based prior" by Shively, T.S. and Khon, R. and Wood, S. J. Amer. Statist. Assoc. 94 447 (1999) 794-797
8. Cantoni E., and Hastie T.J. Degrees of freedom tests for smoothing splines. Biometrika 89 (2002) 251-263
9. Chambers J.M., and Hastie T.J. Statistical Models in S. Computer Science Series (1993), Chapman & Hall, London
10. Chen R., Härdle W., Linton O.B., and Severance-Lossin E. Nonparametric estimation of additive separable regression models. In: Härdle W., and Schimek M.G. (Eds). Statistical Theory and Computational Aspects of Smoothing: Proceedings of the COMPSTAT'94 Satellite Meeting (1996), Heidelberg, Physica-Verlag 247-265
11. Chen, S., Donoho, D., Saunders, M., 1995. Atomic decomposition by basis pursuit. Technical Report 479, Department of Statistics, Stanford University.
12. Chen Z. Fitting multivariate regression functions by interaction spline models. J. Roy. Statist. Soc. Ser. B 55 2 (1993) 473-491
13. Dominici F., McDermott A., Zeger S.L., and Samet J.M. On the use of generalized additive models in time-series studies of air pollution and health. Amer. J. Epidemiol. 156 3 (2002) 193-203
14. Efron B., Hastie T., Johnstone I., and Tibshirani R. Least angle regression. Ann. Statist. 32 2 (2004) 407-499
15. Fu W.J. Penalized regression: the bridge versus the lasso. J. Comput. Graph. Statist. 7 3 (1998) 397-416
16. González-Manteiga W., Quintela-del Río A., and Vieu P. A note on variable selection in nonparametric regression with dependent data. Statist. Probab. Lett. 57 3 (2002) 259-268
17. Grandvalet Y. Least absolute shrinkage is equivalent to quadratic penalization. In: Niklasson L., Bodén M., and Ziemske T. (Eds). ICANN'98 Perspectives in Neural Computing vol. 1 (1998), Springer, Berlin 201-206
18. Grandvalet Y., and Canu S. Outcomes of the equivalence of adaptive ridge with least absolute shrinkage. In: Kearns M.S., Solla S.A., and Cohn D.A. (Eds). Advances in Neural Information Processing Systems vol. 11 (1998), MIT Press, Cambridge, MA 445-451
19. Gu C., and Wahba G. Minimizing GCV/GML scores with multiple smoothing parameters via the newton method. SIAM J. Sci. Statist. Comput. 12 (1991) 383-398
20. Gunn S.R., and Kandola J.S. Structural modeling with sparse kernels. Mach. Learn. 10 (2002) 581-591
21. Guyon I., and Elisseeff A. An introduction to variable and feature selection. J. Mach. Learn. Res. 3 Special Issue on Variable/Feature Selection (2003) 1157-1182
22. Härdle W., and Korostelev A. Search for significant variables in nonparametric additive regression. Biometrika 83 3 (1996) 541-549
23. Hastie T.J., and Tibshirani R.J. Generalized Additive Models, Monographs on Statistics and Applied Probability vol. 43 (1990), Chapman & Hall, London
24. Hastie T.J., Tibshirani R.J., and Friedman J. The Elements of Statistical Learning. Data Mining, Inference and Prediction (2001), Springer Series in Statistics, Springer, New York
25. Hurvich C.M., Simonoff J.S., and Tsai C.L. Smoothing parameter selection in nonparametric regression using an improved akaike information criteria. J. Roy. Statist. Soc. Ser. B 60 2 (1998) 271-293
26. Lin, Y., Zhang, H.H., 2002. Component selection and smoothing in smoothing spline analysis of variance models. Technical Report 1072r, University of Winconsin-Madison and North Carolina State University (Rev janvier 2003).
27. Marx B.D., and Eilers P.H.C. Direct generalized additive modeling with penalized likelihood. Comput. Statist. Data Anal. 28 (1998) 193-209
28. Opsomer J.D., and Ruppert D. A fully automated bandwidth selection method for fitting additive models. J. Multivariate Anal. 73 (1998) 166-179
29. Osborne M.R., Presnell B., and Turlach B.A. On the lasso and its dual. J. Comput. Graph. Statist. 9 2 (2000) 319-337
30. Roth V. Sparse kernel regressors. In: Dorfner G., Bischof H., and Hornik K. (Eds). Artificial Neural Networks-ICANN 2001, Lecture Notes in Computer Science vol. 2130 (2001), Springer, Berlin 339-346
31. Ruppert D., Wand M.P., and Carroll R.J. Semiparametric Regression Cambridge Series on Statistical and Probabilistic Mathematics vol. 12 (2003), Cambridge University Press, Cambridge
32. Shi P., and Tsai C.-L. Semiparametric regression model selections. J. Statist. Plann. Inference 77 1 (1999) 119-139
33. Shively T.S., Khon R., and Wood S. Variable selection and function estimation in additive nonparametric regression using a data-based prior. J. Amer. Statist. Assoc. 99 447 (1999) 777-806
34. Smith M., and Kohn R. Nonparametric regression using Bayesian variable selection. J. Econom. 75 2 (1996) 317-343
35. Stone M. Cross-validatory choice and assessment of statistical predictions. J. Roy. Statist. Soc. Ser. B 36 1 (1974) 111-147
36. Tibshirani R.J. Regression shrinkage and selection via the lasso. J. Roy. Statist. Soc. Ser. B 58 1 (1996) 267-288
37. Wahba G. Spline models for observational data. Regional Conference Series in Applied Mathematics vol. 59 (1990), SIAM, Philadelphia, PA
38. Walker E., and Wright S.P. Comparing curves using additive models. J. Qual. Technol. 34 1 (2002) 118-129
39. Wood S.N. Modelling and smoothing parameter estimation with multiple quadratic penalties. J. Roy. Statist. Soc. Ser. B 62 2 (2000) 413-428
40. Zhang H.H., Wahba G., Lin Y., Voelker M., Ferris M., Klein R., and Klein B. Variable selection and model building via likelihood basis pursuit. J. Amer. Statist. Assoc. 99 (2004) 659-672