  Decision tree learning is increasingly being used for pointwise inference.
Important applications include causal heterogenous treatment effects and
dynamic policy decisions, as well as conditional quantile regression and design
of experiments, where tree estimation and inference is conducted at specific
values of the covariates. In this paper, we call into question the use of
decision trees (trained by adaptive recursive partitioning) for such purposes
by demonstrating that they can fail to achieve polynomial rates of convergence
in uniform norm with non-vanishing probability, even with pruning. Instead, the
convergence may be arbitrarily slow or, in some important special cases, such
as honest regression trees, fail completely. We show that random forests can
remedy the situation, turning poor performing trees into nearly optimal
procedures, at the cost of losing interpretability and introducing two
additional tuning parameters. The two hallmarks of random forests, subsampling
and the random feature selection mechanism, are seen to each distinctively
contribute to achieving nearly optimal performance for the model class
considered.
