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Optimisation of density estimation models with evolutionary algorithms

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Parallel Problem Solving from Nature — PPSN V (PPSN 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1498))

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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).

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References

  1. 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.

    Google Scholar 

  2. S. Geman, E. Bienenstock, and R. Doursat. Neural networks and the bias/variance dilemma. Neural Computation, 4:1–58, 1992.

    Google Scholar 

  3. P. J. Green. On use of the em algorithm for penalized likelihood estimation. J. R. Statist. Soc. B, 52:443–452, 1990.

    MATH  Google Scholar 

  4. J. Moody and C. L. Darken. Fast learning in networks of locally-tuned processing units. Neural Computation, 1:281–294, 1989.

    Google Scholar 

  5. T. Poggio and F. Girosi. Networks for approximation and learning. Proceedings of the IEEE, 78:1481–1497, 1990.

    Article  Google Scholar 

  6. 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.

    Google Scholar 

  7. R. A. Redner and H. F. Walker. Mixture densities, maximum likelihood and the EM algorithm. SIAM Review, 26:195–239, 1984.

    Article  MATH  MathSciNet  Google Scholar 

  8. A. M. Reimetz. Strukturbestimmung von probabilistischen neuronalen Netzen mit Hilfe von Evolutionären Algorithmen. Master's thesis (Diplomarbeit), Fachbereich Statistik, Universität Dortmund, 1998.

    Google Scholar 

  9. 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.

    Google Scholar 

  10. 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.

    MATH  MathSciNet  Google Scholar 

  11. L. D. Whitley. Genetic algorithms and neural networks. In J. Periaux and G. Winter, editors, Genetic Algorithms in Engineering and Computer Science. Wiley, 1995.

    Google Scholar 

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Agoston E. Eiben Thomas Bäck Marc Schoenauer Hans-Paul Schwefel

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© 1998 Springer-Verlag Berlin Heidelberg

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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

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  • DOI: https://doi.org/10.1007/BFb0056941

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  • Print ISBN: 978-3-540-65078-2

  • Online ISBN: 978-3-540-49672-4

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