Abstract
We propose a new optimisation method for estimating both the parameters and the structure, i. e. the number of components, of a finite mixture model for density estimation. We employ a hybrid method consisting of an evolutionary algorithm for structure optimisation in conjunction with a gradient-based method for evaluating each candidate model architecture. For structure modification we propose specific, problem dependent evolutionary operators. The introduction of a regularisation term prevents the models from over-fitting the data. Experiments show good generalisation abilities of the optimised structures.
Supported by the BMBF under Grant No. 01IB701A0 (SONN II).
Preview
Unable to display preview. Download preview PDF.
References
B. Carse and T. C. Fogarty. Fast evolutionary learning of minimal radial basis function neural networks using a genetic algorithm. In T. C. Fogarty, editor, Evolutionary Computing — selected papers from AISB, pages 1–22. Springer, 1996.
S. Geman, E. Bienenstock, and R. Doursat. Neural networks and the bias/variance dilemma. Neural Computation, 4:1–58, 1992.
P. J. Green. On use of the em algorithm for penalized likelihood estimation. J. R. Statist. Soc. B, 52:443–452, 1990.
J. Moody and C. L. Darken. Fast learning in networks of locally-tuned processing units. Neural Computation, 1:281–294, 1989.
T. Poggio and F. Girosi. Networks for approximation and learning. Proceedings of the IEEE, 78:1481–1497, 1990.
W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery. Numerical Recipes in C: The Art of Scientific Computing. Cambridge University Press, 1992.
R. A. Redner and H. F. Walker. Mixture densities, maximum likelihood and the EM algorithm. SIAM Review, 26:195–239, 1984.
A. M. Reimetz. Strukturbestimmung von probabilistischen neuronalen Netzen mit Hilfe von Evolutionären Algorithmen. Master's thesis (Diplomarbeit), Fachbereich Statistik, Universität Dortmund, 1998.
B. Sendhoff, M. Kreutz, and W. von Seelen. A condition for the genotype-phenotype mapping: Causality. In T. Bäck, editor, Proc. International Conference on Genetic Algorithms, pages 73–80. Morgan Kaufman, 1997.
B. W. Silverman, M. C. Jones, J. D. Wilson, and D. W. Nychka. A smoothed em approach to indirect estimation problems, with particular reference to stereology and emission tomography. J. R. Statist. Soc. B, 52:271–324, 1990.
L. D. Whitley. Genetic algorithms and neural networks. In J. Periaux and G. Winter, editors, Genetic Algorithms in Engineering and Computer Science. Wiley, 1995.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kreutz, M., Reimetz, A.M., Sendhoff, B., Weihs, C., von Seelen, W. (1998). Optimisation of density estimation models with evolutionary algorithms. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, HP. (eds) Parallel Problem Solving from Nature — PPSN V. PPSN 1998. Lecture Notes in Computer Science, vol 1498. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0056941
Download citation
DOI: https://doi.org/10.1007/BFb0056941
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-65078-2
Online ISBN: 978-3-540-49672-4
eBook Packages: Springer Book Archive