Improving the kernel regularized least squares method for small-sample regression

Neurocomputing

Volumn 163, Issue , 2015, Pages 106-114

  Braga, Igor ^a   Monard, Maria Carolina ^a  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

Cross validation; Kernel regularizedleast squares; Non linear regression; Parameter selection; RBF kernel; Spline kernel

Indexed keywords

ADDITIVES; REGRESSION ANALYSIS;

CROSS VALIDATION; KERNEL REGULARIZEDLEAST SQUARES; NON-LINEAR REGRESSION; PARAMETER SELECTION; RBF KERNELS; SPLINE KERNELS;

LEAST SQUARES APPROXIMATIONS;

ARTICLE; FINITE PREDICTION ERROR; KERNEL METHOD; KERNEL REGULARIZED LEAST SQUARE METHOD; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; MATHEMATICAL PARAMETERS; NONLINEAR REGRESSION ANALYSIS; PRIORITY JOURNAL; STATISTICAL MODEL; STATISTICAL PARAMETERS; VALIDATION PROCESS;

EID: 84930276942     PISSN: 09252312     EISSN: 18728286     Source Type: Journal    
DOI: 10.1016/j.neucom.2014.12.097     Document Type: Article

References (19)

1. Schölkopf B., Smola A.J. Learning With Kernels: Support Vector Machines, Regularization, Optimization and Beyond 2002, MIT Press, Cambridge, Mass., USA.
2. G. Wahba, Spline Models for Observational Data, CBMS-NSF Regional Conference Series in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Penn., USA, 1990.
3. F. Girosi, An Equivalence Between Sparse Approximation and Support Vector Machines, Technical Report, Massachusetts Institute of Technology, 1997. http://cbcl.mit.edu/publications/ai-publications/1500-1999/AIM-1606.ps.
4. R.M. Rifkin, Everything old is new again: a fresh look at historical approaches in machine learning (Ph.D. thesis), MIT-Sloan School of Management, 2006. URL . http://dspace.mit.edu/bitstream/handle/1721.1/17549/51896466.pdf?sequence=1.
5. Vapnik V. Statistical Learning Theory 1998, Wiley-Interscience, New York, NY, USA.
6. Steinwart I. On the influence of the kernel on the consistency of support vector machines. J. Mach. Learn. Res. 2001, 2:67-93.
7. R. Izmailov, V. Vapnik, A. Vashist, Multidimensional splines with infinite number of knots as SVM kernels, in: IJCNN '13: Proceedings of the 2013 International Joint Conference on Neural Networks, 2013, pp. 1-7.
8. Kimeldorf G., Wahba G. A correspondence between Bayesian estimation on stochastic processes and smoothing by splines. Ann. Math. Stat. 1970, 41(2):495-502.
9. Luntz A., Brailovsky V. On estimation of characters obtained in statistical procedure of recognition. Techn. Kibern. 1969, 3. (in Russian).
10. Akaike H. Statistical predictor identification. Ann. Inst. Stat. Math. 1970, 22(1):203-217.
11. Wahba G., Craven P. Smoothing noisy data with spline functions. estimating the correct degree of smoothing by the method of generalized cross-validation. Numer. Math. 1979, 31:377-404.
12. Schwarz G. Estimating the dimension of a model. Ann. Stat. 1978, 6(2):461-464.
13. Shibata R. An optimal selection of regression variables. Biometrika 1981, 68(1):45-54.
14. Cherkassky V., Shao X., Mulier F., Vapnik V. Model complexity control for regression using VC generalization bounds. IEEE Trans. Neural Netw. 1999, 10(5):1075-1089.
15. Hastie T.J., Tibshirani R.J. Generalized Additive Models, CRC Monographs on Statistics and Applied Probability 1990, Chapman and Hall, Boca Raton, FL, USA.
16. D. Schuurmans, A new metric-based approach to model selection, in: AAAI '97: Proceedings of the Fourteenth National Conference on Artificial Intelligence, 1997, pp. 552-558.
17. Schuurmans D., Southey F., Wilkinson D., Guo Y. Metric-based Approaches for Semi-supervised Regression and Classification, Adaptive Computation and Machine Learning 2006, MIT Press, pp. 421-451.
18. Chapelle O., Vapnik V., Bengio Y. Model selection for small sample regression. Mach. Learn. 2002, 48(1-3):9-23.
19. Alcalá-Fernández J., Fernández A., Luengo J., Derrac J., García S., Sánchez L., Herrera F. KEEL data-mining software tool. data set repository, integration of algorithms and experimental analysis framework. J. Mult. Valued Logic Soft Comput. 2011, 17(2-3):255-287.