  For low-dimensional data sets with a large amount of data points, standard
kernel methods are usually not feasible for regression anymore. Besides simple
linear models or involved heuristic deep learning models, grid-based
discretizations of larger (kernel) model classes lead to algorithms, which
naturally scale linearly in the amount of data points. For moderate-dimensional
or high-dimensional regression tasks, these grid-based discretizations suffer
from the curse of dimensionality. Here, sparse grid methods have proven to
circumvent this problem to a large extent. In this context, space- and
dimension-adaptive sparse grids, which can detect and exploit a given low
effective dimensionality of nominally high-dimensional data, are particularly
successful. They nevertheless rely on an axis-aligned structure of the solution
and exhibit issues for data with predominantly skewed and rotated coordinates.
  In this paper we propose a preprocessing approach for these adaptive sparse
grid algorithms that determines an optimized, problem-dependent coordinate
system and, thus, reduces the effective dimensionality of a given data set in
the ANOVA sense. We provide numerical examples on synthetic data as well as
real-world data to show how an adaptive sparse grid least squares algorithm
benefits from our preprocessing method.
