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Conference of the Spanish Association for Artificial Intelligence

CAEPIA 2007: Current Topics in Artificial Intelligence pp 190–199Cite as

Finiteness Properties of Some Families of GP-Trees

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4788))

Abstract

We provide upper bounds for the Vapnik-Chervonenkis dimension of classes of subsets of that can be recognized by computer programs built from arithmetical assignments, infinitely differentiable algebraic operations (like k-root extraction and, more generally, operations defined by algebraic series of fractional powers), conditional statements and while instructions. This includes certain classes of GP-trees considered in Genetic Programming for symbolic regression and bi-classification. As a consequence we show explicit quantitative properties that can help to design the fitness function of a GP learning machine.

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Author information

Authors and Affiliations

  1. Centro de Inteligencia Artificial, Universidad de Oviedo, Campus de Viesques, 33271 Gijón, Spain

    César L. Alonso

  2. Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, 39005 Santander, Spain

    José Luis Montaña

Authors
  1. César L. Alonso
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  2. José Luis Montaña
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Editor information

Daniel Borrajo Luis Castillo Juan Manuel Corchado

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© 2007 Springer-Verlag Berlin Heidelberg

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Alonso, C.L., Montaña, J.L. (2007). Finiteness Properties of Some Families of GP-Trees. In: Borrajo, D., Castillo, L., Corchado, J.M. (eds) Current Topics in Artificial Intelligence. CAEPIA 2007. Lecture Notes in Computer Science(), vol 4788. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75271-4_20

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  • DOI: https://doi.org/10.1007/978-3-540-75271-4_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-75270-7

  • Online ISBN: 978-3-540-75271-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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