  Kernels ensuing from tree ensembles such as random forest (RF) or gradient
boosted trees (GBT), when used for kernel learning, have been shown to be
competitive to their respective tree ensembles (particularly in higher
dimensional scenarios). On the other hand, it has been also shown that
performance of the kernel algorithms depends on the degree of the kernel-target
alignment. However, the kernel-target alignment for kernel learning based on
the tree ensembles has not been investigated and filling this gap is the main
goal of our work.
  Using the eigenanalysis of the kernel matrix, we demonstrate that for
continuous targets good performance of the tree-based kernel learning is
associated with strong kernel-target alignment. Moreover, we show that well
performing tree ensemble based kernels are characterized by strong target
aligned components that are expressed through scalar products between the
eigenvectors of the kernel matrix and the target. This suggests that when tree
ensemble based kernel learning is successful, relevant information for the
supervised problem is concentrated near lower dimensional manifold spanned by
the target aligned components. Persistence of the strong target aligned
components in tree ensemble based kernels is further supported by sensitivity
analysis via landmark learning. In addition to a comprehensive simulation
study, we also provide experimental results from several real life data sets
that are in line with the simulations.
