  Tree based ensembles such as Breiman's random forest (RF) and Gradient
Boosted Trees (GBT) can be interpreted as implicit kernel generators, where the
ensuing proximity matrix represents the data-driven tree ensemble kernel.
Kernel perspective on the RF has been used to develop a principled framework
for theoretical investigation of its statistical properties. Recently, it has
been shown that the kernel interpretation is germane to other tree-based
ensembles e.g. GBTs. However, practical utility of the links between kernels
and the tree ensembles has not been widely explored and systematically
evaluated.
  Focus of our work is investigation of the interplay between kernel methods
and the tree based ensembles including the RF and GBT. We elucidate the
performance and properties of the RF and GBT based kernels in a comprehensive
simulation study comprising of continuous and binary targets. We show that for
continuous targets, the RF/GBT kernels are competitive to their respective
ensembles in higher dimensional scenarios, particularly in cases with larger
number of noisy features. For the binary target, the RF/GBT kernels and their
respective ensembles exhibit comparable performance. We provide the results
from real life data sets for regression and classification to show how these
insights may be leveraged in practice. Overall, our results support the tree
ensemble based kernels as a valuable addition to the practitioner's toolbox.
  Finally, we discuss extensions of the tree ensemble based kernels for
survival targets, interpretable prototype and landmarking classification and
regression. We outline future line of research for kernels furnished by
Bayesian counterparts of the frequentist tree ensembles.
