CRANFIELD UNIVERSITY Eleni Anthippi Chatzimichali ...

In the example of Figure 3-5, the Box complex algorithm performed 14 iterations and
54 function evaluations in total before successfully identifying the optimal
combination of hyperparameters. The initial combination of and produced an
average bootstrapping test error equal to 0.31. After the application of the Box
complex algorithm, the bootstrapping error decreased to 0.28. Based on the plots, the
simplices become extremely small as they contract towards the minimum. In the final
plot, no further improvement can be performed. Based on the graphs of Figure 3-5,
we can conclude that the optimal combination of hyperparameters is indeed identified
within robust areas of the grid.
The optimisation results of Figure 3-5 derive from a single classifier. For the entire
classification ensemble (100 individual classifiers), the optimal hyperparameters as
selected by the Box complex algorithm are illustrated in Figure 3-6. In order to
highlight any underlying patterns, the plots include contours of density estimations. It
is interesting to note that only three out of 100 points are further apart from the rest
and may be located in unacceptable regions with high prediction error.
Figure 3-6 Contour plots of the density estimation of the optimal hyperparameters as defined by
the Box complex algorithm
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