  Random forests are ensemble methods which grow trees as base learners and
combine their predictions by averaging. Random forests are known for their good
practical performance, particularly in high dimensional set-tings. On the
theoretical side, several studies highlight the potentially fruitful connection
between random forests and kernel methods. In this paper, we work out in full
details this connection. In particular, we show that by slightly modifying
their definition, random forests can be rewrit-ten as kernel methods (called
KeRF for Kernel based on Random Forests) which are more interpretable and
easier to analyze. Explicit expressions of KeRF estimates for some specific
random forest models are given, together with upper bounds on their rate of
consistency. We also show empirically that KeRF estimates compare favourably to
random forest estimates.
