Density estimation with genetic programming for inverse problem solving

  • Authors:

  • Michael Defoin Platel;Sébastien Vérel;Manuel Clergue;Malik Chami

  • Affiliations:

  • Laboratoire I3S, CNRS, Université de Nice Sophia Antipolis, France and Laboratoire d'Océanographie de Villefranche sur Mer, CNRS-Université Pierre et Marie Curie-Paris 6, France;Laboratoire d'Océanographie de Villefranche sur Mer, CNRS-Université Pierre et Marie Curie-Paris 6, France;Laboratoire d'Océanographie de Villefranche sur Mer, CNRS-Université Pierre et Marie Curie-Paris 6, France;Laboratoire I3S, CNRS, Université de Nice Sophia Antipolis, France

  • Venue:
  • EuroGP'07 Proceedings of the 10th European conference on Genetic programming
  • Year:
  • 2007

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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.