Genetic Algorithms as Tool for Statistical Analysis of High-Dimensional Data Structures - Softcover

Krause, R�diger

9783832506612: Genetic Algorithms as Tool for Statistical Analysis of High-Dimensional Data Structures

Softcover

ISBN 10: 3832506616 ISBN 13: 9783832506612

Verlag: Logos Berlin, 2004

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In regression the objective is to determine an appropriate function
which reflects reality as accurate as possible but also eliminates
irregularities from data noise and is therefore easy to interpret.
A popular and flexible approach for estimating the true underlying
function is the additive model. One possible approach for fitting
additive models is the expansion in B-splines which allows direct
calculation of the estimators. If the number of B-splines is too
large the estimated functions become wiggly and tend to be very
close to the observed data. To avoid this problem of overfitting
we use a penalization approach characterized by smoothing parameters.
In this thesis we propose the use of genetic algorithms
for smoothing parameter optimization. Genetic algorithms are rarely
applied in the field of statistics and refer to the principle that
better adapted individuals win against their competitors
under equal conditions. Apart from smoothing parameter
optimization the user often faces datasets containing large numbers
of relevant and irrelevant explanatory variables. Appropriate variable
selection approaches allow to reduce the number of variables to
subsets of relevant variables. We propose to consider the problems of
variable selection and choice of smoothing parameters simultaneously
by using genetic algorithms. Our approach bases on an appropriate
combination of the genetic algorithms for smoothing parameter
optimization and variable selection.