  A random forest is a popular tool for estimating probabilities in machine
learning classification tasks. However, the means by which this is accomplished
is unprincipled: one simply counts the fraction of trees in a forest that vote
for a certain class. In this paper, we forge a connection between random
forests and kernel regression. This places random forest probability estimation
on more sound statistical footing. As part of our investigation, we develop a
model for the proximity kernel and relate it to the geometry and sparsity of
the estimation problem. We also provide intuition and recommendations for
tuning a random forest to improve its probability estimates.
