Jennifer Pittman, Pennsylvania State University
Adaptive Splines and Genetic Algorithms for Optimal Statistical
Modeling
Due in part to the increased availability of
computational power, spatially adaptive smoothing methods involving
regression splines have become a rapidly developing class of
nonparametric modeling techniques. Most existing algorithms for
fitting adaptive splines are based on non-linear optimization and/or
stepwise selection. Although computationally fast and spatially
adaptive, stepwise knot selection is necessarily suboptimal while
determining the best model over the space of adaptive knot splines is
a very poorly behaved non-linear optimization problem. A possible
alternative is to use more intensive numerical optimization techniques
such as genetic algorithms to perform knot selection. A spatially
adaptive modeling technique referred to as adaptive genetic splines
(AGS) is introduced which combines the optimization power of a genetic
algorithm with the flexibility of polynomial splines. Preliminary
simulation results comparing the performance of the genetic algorithm
method to other current methods, such as HAS (Luo and Wahba 1997) and
SUREshrink (Donoho and Johnstone 1995), will be discussed, as well as
a current application of AGS in the engineering sciences. Topics for
future research will also be mentioned.