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Selecção de variáveis em estatística multivariada
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Autores
Orientador(es)
Resumo(s)
The problem of variable selection consists in identifying a k-subset of a set of
original variables that is optimal for a given criterion of adequate approximation to the
whole data set.
In this work we present and we discuss some new optimization criteria and others
that are suggested by the literature. We present and we discuss the algorithms for the
optimization problems resulting from the different criteria, as well as the calculated
computational results.
The criteria and algorithms are available in the package Subselect that is called from
statistical program R. This package is in permanent update, with varied contributions,
between which, this work is included. Package and program are of the public domain
and meet available in the Internet.
In this work we also discuss a multiple criteria optimization for the problem of
identifying subsets of variables. In this approach, we are looking for subsets that are
optimal for some criteria simultaneously. The induced total order for an only criterion
gives place to a partial order, with which is associated a set of solutions that cannot
simultaneously be improved in all the criteria. Usually they are called maximal, efficient
solutions or Pareto optimal.
Descrição
Doutoramento em Matemática e Estatística - Instituto Superior de Agronomia
Palavras-chave
variable selection multivariate statistics combinatorial optimization Heuristics Pareto optimal