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A Statistical Learning Perspective of Genetic Programming

Merve Amil 1, 2 Nicolas Bredeche 1, 2 Christian Gagné 1, 2 Sylvain Gelly 1, 2 Marc Schoenauer 1, 2 Olivier Teytaud 1, 2 
2 TAO - Machine Learning and Optimisation
LRI - Laboratoire de Recherche en Informatique, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR8623
Abstract : This paper proposes a theoretical analysis of Genetic Programming (GP) from the perspective of statistical learning theory, a well grounded mathematical toolbox for machine learning. By computing the Vapnik-Chervonenkis dimension of the family of programs that can be inferred by a specific setting of GP, it is proved that a parsimonious fitness ensures universal consistency. This means that the empirical error minimization allows convergence to the best possible error when the number of test cases goes to infinity. However, it is also proved that the standard method consisting in putting a hard limit on the program size still results in programs of infinitely increasing size in function of their accuracy. It is also shown that cross-validation or hold-out for choosing the complexity level that optimizes the error rate in generalization also leads to bloat. So a more complicated modification of the fitness is proposed in order to avoid unnecessary bloat while nevertheless preserving universal consistency.
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Submitted on : Saturday, March 21, 2009 - 9:09:26 AM
Last modification on : Sunday, June 26, 2022 - 11:49:33 AM
Long-term archiving on: : Thursday, June 10, 2010 - 5:57:51 PM


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  • HAL Id : inria-00369782, version 1



Merve Amil, Nicolas Bredeche, Christian Gagné, Sylvain Gelly, Marc Schoenauer, et al.. A Statistical Learning Perspective of Genetic Programming. EuroGP, 2009, Tuebingen, Germany. pp.327-338. ⟨inria-00369782⟩



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