  Assume we are given a set of items from a general metric space, but we
neither have access to the representation of the data nor to the distances
between data points. Instead, suppose that we can actively choose a triplet of
items (A,B,C) and ask an oracle whether item A is closer to item B or to item
C. In this paper, we propose a novel random forest algorithm for regression and
classification that relies only on such triplet comparisons. In the theory part
of this paper, we establish sufficient conditions for the consistency of such a
forest. In a set of comprehensive experiments, we then demonstrate that the
proposed random forest is efficient both for classification and regression. In
particular, it is even competitive with other methods that have direct access
to the metric representation of the data.
