Finiteness Properties of Some Families of GP-Trees

Authors:
César L. Alonso;José Luis Montaña
Affiliations:
Centro de Inteligencia Artificial, Universidad de Oviedo, Campus de Viesques, 33271 Gijón, Spain;Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, 39005 Santander, Spain
Venue:
Current Topics in Artificial Intelligence
Year:
2007

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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, infinitelydifferentiable algebraic operations(like k-root extraction and, more generally, operations defined by algebraic series of fractional powers), conditional statementsand 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.