  Exploratory landscape analysis (ELA) supports supervised learning approaches
for automated algorithm selection and configuration by providing sets of
features that quantify the most relevant characteristics of the optimization
problem at hand. In black-box optimization, where an explicit problem
representation is not available, the feature values need to be approximated
from a small number of sample points. In practice, uniformly sampled random
point sets and Latin hypercube constructions are commonly used sampling
strategies. In this work, we analyze how the sampling method and the sample
size influence the quality of the feature value approximations and how this
quality impacts the accuracy of a standard classification task. While, not
unexpectedly, increasing the number of sample points gives more robust
estimates for the feature values, to our surprise we find that the feature
value approximations for different sampling strategies do not converge to the
same value. This implies that approximated feature values cannot be interpreted
independently of the underlying sampling strategy. As our classification
experiments show, this also implies that the feature approximations used for
training a classifier must stem from the same sampling strategy as those used
for the actual classification tasks. As a side result we show that classifiers
trained with feature values approximated by Sobol' sequences achieve higher
accuracy than any of the standard sampling techniques. This may indicate
improvement potential for ELA-trained machine learning models.
