  A random forest prediction can be computed by the scalar product of the
labels of the training examples and a set of weights that are determined by the
leafs of the forest into which the test object falls; each prediction can hence
be explained exactly by the set of training examples for which the weights are
non-zero. The number of examples used in such explanations is shown to vary
with the dimensionality of the training set and hyperparameters of the random
forest algorithm. This means that the number of examples involved in each
prediction can to some extent be controlled by varying these parameters.
However, for settings that lead to a required predictive performance, the
number of examples involved in each prediction may be unreasonably large,
preventing the user to grasp the explanations. In order to provide more useful
explanations, a modified prediction procedure is proposed, which includes only
the top-weighted examples. An investigation on regression and classification
tasks shows that the number of examples used in each explanation can be
substantially reduced while maintaining, or even improving, predictive
performance compared to the standard prediction procedure.
