  Random forests remain among the most popular off-the-shelf supervised
learning algorithms. Despite their well-documented empirical success, however,
until recently, few theoretical results were available to describe their
performance and behavior. In this work we push beyond recent work on
consistency and asymptotic normality by establishing rates of convergence for
random forests and other supervised learning ensembles. We develop the notion
of generalized U-statistics and show that within this framework, random forest
predictions can potentially remain asymptotically normal for larger subsample
sizes than previously established. We also provide Berry-Esseen bounds in order
to quantify the rate at which this convergence occurs, making explicit the
roles of the subsample size and the number of trees in determining the
distribution of random forest predictions.
