Simultaneous Selection of Variables and Smoothing Parameters in Additive Models
For additive models of the type y = f1(x1) + … + fP(xp) + ε where fj,j = 1, …, p, have unspecified functional form the problem of variable selection is strongly connected to the choice of the amount of smoothing used for components fj. In this paper we propose the simultaneous choice of variables and smoothing parameters based on genetic algorithms. Common genetic algorithms have to be modified since inclusion of variables and smoothing have to be coded separately but are linked in the search for optimal solutions. The basic tool for fitting the additive model is the expansion in B-splines. This approach allows for direct estimates which is essential for the method to work.
KeywordsGenetic Algorithm Variable Selection Smoothing Parameter Parent String Parameter String
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- DE BOOR, C. (1978): A Practical Guide to Splines. Springer, New York, Heidelberg, Berlin.Google Scholar
- GOLDBERG, D.E. (1989): Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Reading, MA.Google Scholar
- HASTIE, T. and TIBSHIRANI, R. (1990): Generalized Additive Models. Chapman and Hall, London.Google Scholar
- KRAUSE, R. and TUTZ, G. (2003): Additive Modeling with Penalized Regression Splines and Genetic Algorithms. Discussion Paper Nr. 312, SFB 386, Ludwig Maximilians-Universität München.Google Scholar
- MICHALEWICZ, Z. (1996): Genetic Algorithms + Data Structures = Evolution Programs. Springer, Berlin.Google Scholar
- MITCHELL, M. (1996): An Introduction to Genetic Algorithms. MIT Press, Cambridge, MassachusettsGoogle Scholar
- WOOD, S. (2001): mgcv: GAMs and Generalized Ridge Regression for R. Rnews, 1(2), 20–25.Google Scholar