  The last decade has shed some light on theoretical properties such as their
consistency for regression tasks. In the current paper, we propose a new class
of very simple learners based on so-called naive trees. These naive trees
partition the feature space completely at random and independent of the data.
Although counter-intuitive, we prove these naive trees and ensembles are
consistent under fairly general assumptions. However, naive trees appear to be
too simple for actual application. We therefore analyze their finite sample
properties in a simulation and small benchmark study. We find a slow
convergence speed and a rather poor predictive performance. Based on these
results, we finally discuss to what extent consistency proofs help to justify
the application of complex learning algorithms.
