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Density Estimation with Genetic Programming for Inverse Problem Solving

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Genetic Programming (EuroGP 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4445))

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Abstract

This paper addresses the resolution, by Genetic Programming (GP) methods, of ambiguous inverse problems, where for a single input, many outputs can be expected. We propose two approaches to tackle this kind of many-to-one inversion problems, each of them based on the estimation, by a team of predictors, of a probability density of the expected outputs. In the first one, Stochastic Realisation GP, the predictors outputs are considered as the realisations of an unknown random variable which distribution should approach the expected one. The second one, Mixture Density GP, directly models the expected distribution by the mean of a Gaussian mixture model, for which genetic programming has to find the parameters. Encouraging results are obtained on four test problems of different difficulty, exhibiting the interests of such methods.

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Authors and Affiliations

  1. Laboratoire I3S, CNRS-Université de Nice Sophia Antipolis, France

    Michael Defoin Platel & Malik Chami

  2. Laboratoire d’Océanographie de Villefranche sur Mer, CNRS-Université Pierre et Marie Curie-Paris6, France

    Michael Defoin Platel, Sébastien Vérel & Manuel Clergue

Authors
  1. Michael Defoin Platel
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  2. Sébastien Vérel
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  3. Manuel Clergue
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  4. Malik Chami
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Editor information

Marc Ebner Michael O’Neill Anikó Ekárt Leonardo Vanneschi Anna Isabel Esparcia-Alcázar

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© 2007 Springer Berlin Heidelberg

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Defoin Platel, M., Vérel, S., Clergue, M., Chami, M. (2007). Density Estimation with Genetic Programming for Inverse Problem Solving. In: Ebner, M., O’Neill, M., Ekárt, A., Vanneschi, L., Esparcia-Alcázar, A.I. (eds) Genetic Programming. EuroGP 2007. Lecture Notes in Computer Science, vol 4445. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71605-1_5

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  • DOI: https://doi.org/10.1007/978-3-540-71605-1_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-71602-0

  • Online ISBN: 978-3-540-71605-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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