Finiteness properties of some families of GP-trees

  1. Alonso, César L. 1
  2. Montaña, José Luis 2
  1. 1 Universidad de Oviedo
    info

    Universidad de Oviedo

    Oviedo, España

    ROR https://ror.org/006gksa02

  2. 2 Universidad de Cantabria
    info

    Universidad de Cantabria

    Santander, España

    ROR https://ror.org/046ffzj20

Book:
XII Conferencia de la Asociación Española para la Inteligencia Artificial: (CAEPIA 2007). Actas
  1. Borrajo Millán, Daniel (coord.)
  2. Castillo Vidal, Luis (coord.)
  3. Corchado Rodríguez, Juan Manuel (coord.)

Publisher: Universidad de Salamanca

ISBN: 978-84-611-8846-8,  978-84-611-8847-5

Year of publication: 2007

Volume: 1

Pages: 107-116

Congress: Conferencia de la Asociación Española para la Inteligencia Artificial (12. 2007. Salamanca)

Type: Conference paper

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Abstract

We provide upper bounds for the Vapnik-Chervonenkis dimension of classes of subsets of IRn 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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