Model building with likelihood basis pursuit

Optimization Methods and Software

Volumn 19, Issue 5 SPEC. ISS., 2004, Pages 577-594

  Ferris, Michael C ^a   Voelker, Meta M ^a   Zhang, Hao Helen ^b  

^a University of Wisconsin   (United States)

^b NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

Basis pursuit; Model building; Parameter selection; Slice models

Indexed keywords

APPROXIMATION THEORY; FUNCTIONS; INTEGER PROGRAMMING; MATHEMATICAL MODELS; PARAMETER ESTIMATION; PROBABILITY; PROBLEM SOLVING; SET THEORY;

BASIS PURSUIT; MODEL BUILDING; PARAMETER SELECTION; SLICE MODELS;

MAXIMUM LIKELIHOOD ESTIMATION;

EID: 6344261712     PISSN: 10556788     EISSN: None     Source Type: Journal    
DOI: 10.1080/1055678042000221719     Document Type: Article

References (31)

1. O.L. Mangasarian (2000). Generalized support vector machines. In: A. Smola, P. Bartlett, B. Schölkopf and D. Schuurmans (Eds.), Advances in Large Margin Classifiers, pp. 135-146. MIT Press, Cambridge, Massachusetts.
2. G. Fung, O.L. Mangasarian and A. Smola (2002). Minimal kernel classifiers. Journal of Machine Learning Research, 303-321.
3. G. Johnston (1993). SAS software to fit the generalized linear model. In SUGI Proceedings. Available as PDF document from http://www.sas.com/rnd/app/ papers/abstracts/genmod.html.
4. R.J. Tibshirani (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society, B, 58, 267-288.
5. H. Zhang, G. Wahba, Y. Lin, M. Voelker, M. Ferris, R. Klein and B. Klein (2004). Variable selection and model building via likelihood basis pursuit. Journal of American Statistical Association, forthcoming.
6. P.S. Bradley and O.L. Mangasarian (1998). Feature selection via concave minimization and support vector machines. In: J. Shavlik, (Ed.), Machine Learning Proceedings of the Fifteenth International Conference(ICML'98), pp. 82-90, Morgan Kaufmann, San Francisco, California. ftp://ftp.cs.wisc.edu/math- prog/tech-reports/98-03.ps.
7. O.L. Mangasarian and D.R. Musicant (2000). Robust linear and support vector regression. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22, 950-955.
8. M.C. Ferris and M.M. Voelker (2002). Slice models in general purpose modeling systems: An application to DEA. Optimization Methods and Software, 17, 1009-1032.
9. M.M. Voelker (2002). Optimization of Slice Models. PhD thesis, University of Wisconsin, Madison, Wisconsin.
10. Y. Lin, G. Wahba, H. Zhang and Y. Lee (2002). Statistical properties and adaptive tuning of support vector machines. Machine Learning, 48, 115-136.
11. G. Wahba, Y. Wang, C. Gu, R. Klein and B. Klein (1995). Smooth spline ANOVA for exponential families, with application to the Wisconsin epidemiological study of diabetic retinopathy. Annals of Statistics, 23(6), 1865-1895.
12. H. Zhang, G. Wahba, Y. Lin, M. Voelker, M. Ferris, R. Klein and B. Klein (2001). Variable selection via basis pursuit for non-Gaussian data. In 2001 Proceedings of the American Statistical Association, Biometrics Section [CDROM], American Statistical Association, Alexandria, VA.
13. D. Xiang and G. Wahba (1998). Approximate smoothing spline methods for large data sets in the binary case. In Proceedings of ASA Joint Statistical Meetings, Biometrics Section, pp. 94-99.
14. D. Ruppert and R.J. Carroll (2000). Spatially-adaptive penalties for spline fitting. Australian and New Zealand Journal of Statistics, 45, 205-223.
15. P. Yau, R. Kohn and S. Wood (2003). Bayesian variable selection and model averaging in high dimensional multinomial nonparametric regression. Journal of Computational and Graphical Statistics, 12, 23-54.
16. Y-J. Lee and O.L. Mangasarian (2000), Reduced support vector machines. Data Mining Institute Technical Report 00-07, Computer Sciences Department, University of Wisconsin, Madison, Wisconsin, 2000. Appeared in CD Proceedings of the SIAM International Conference on Data Mining, Chicago, April 5-7, 2001, SIAM.
17. G. Wahba (1990). Spline Models for Observational Data. SIAM, Philadelphia, PA.
18. S.S. Chen, D.L. Donoho and M.A. Saunders (1998). Atomic decomposition by basis pursuit. SIAM Journal on Scientific Computing, 20, 33-61.
19. X. Lin, G. Wahba, D. Xiang, F. Gao, R. Klein and B. Klein (2000). Smoothing spline ANOVA models for large data sets with Bernoulli observations and the randomized GACV. The Annals of Statistics, 28, 1570-1600.
20. C. Gu (2002). Smoothing spline ANOVA models. Springer-Verlag.
21. H. Zhang (2002). Nonparametric Variable Selection and Model Building Via Likelihood Basis Pursuit. PhD thesis, Department of Statistics, University of Wisconsin, Madison, WI.
22. D. Girard (1998). Asymptotic comparison of (partial) cross-validation, GCV and randomized GCV in nonparametric regression. The Annals of Statistics, 26, 315-334.
23. M. Hutchinson (1989). A stochastic estimator for the trace of the influence matrix for Laplacian smoothing splines. Commun. Statist.-Simula., 18, 1059-1076.
24. B.A. Murtagh and M.A. Saunders (1983). MINOS 5.0 user's guide. Technical Report SOL 83.20, Systems Optimization Laboratory, Department of Operations Research, Stanford University, Stanford, California. Available as PDF document from http://www.sbsi-sol-optimize.com/manuals.htm.
25. J.A. Nelder and R. Mead (1965). A simplex method for function minimization. Computer Journal, 7, 308-313.
26. J.C. Lagarias, J.A. Reeds, M.H. Wright and P.E. Wright (1998). Convergence of the Nelder-Mead simplex method in low dimensions. SIAM Journal on Optimization, 9, 112-147.
27. M.J.D. Powell (2002). UOBYQA: unconstrained optimization by quadratic approximation. Mathematical Programming, 92, 555-582.
28. M. Marazzi and J. Nocedal (2002). Wedge trust region methods for derivative free optimization. Mathematical Programming, 91, 289-305.
29. MathWorks, Inc. FMINSEARCH. MATLAB function. Obtained from the MATLAB command 'type fminsearch' (October 2002).
30. M.J.D. Powell. Private communication via email, November 2001.
31. Marcelo Marazzi. Private communication via email, October 2001.