  Breiman's random forest (RF) can be interpreted as an implicit kernel
generator,where the ensuing proximity matrix represents the data-driven RF
kernel. Kernel perspective on the RF has been used to develop a principled
framework for theoretical investigation of its statistical properties. However,
practical utility of the links between kernels and the RF has not been widely
explored and systematically evaluated.Focus of our work is investigation of the
interplay between kernel methods and the RF. We elucidate the performance and
properties of the data driven RF kernels used by regularized linear models in a
comprehensive simulation study comprising of continuous, binary and survival
targets. We show that for continuous and survival targets, the RF kernels are
competitive to RF in higher dimensional scenarios with larger number of noisy
features. For the binary target, the RF kernel and RF exhibit comparable
performance. As the RF kernel asymptotically converges to the Laplace kernel,
we included it in our evaluation. For most simulation setups, the RF and
RFkernel outperformed the Laplace kernel. Nevertheless, in some cases the
Laplace kernel was competitive, showing its potential value for applications.
We also provide the results from real life data sets for the regression,
classification and survival to illustrate how these insights may be leveraged
in practice.Finally, we discuss further extensions of the RF kernels in the
context of interpretable prototype and landmarking classification, regression
and survival. We outline future line of research for kernels furnished by
Bayesian counterparts of the RF.
