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Decision tree learning is increasingly being used for pointwise inference.Important applications include causal heterogenous treatment effects anddynamic policy decisions, as well as conditional quantile regression and designof experiments, where tree estimation and inference is conducted at specificvalues of the covariates. In this paper, we call into question the use ofdecision trees (trained by adaptive recursive partitioning) for such purposesby demonstrating that they can fail to achieve polynomial rates of convergencein uniform norm, even with pruning. Instead, the convergence may bepoly-logarithmic or, in some important special cases, such as honest regressiontrees, fail completely. We show that random forests can remedy the situation,turning poor performing trees into nearly optimal procedures, at the cost oflosing interpretability and introducing two additional tuning parameters. Thetwo hallmarks of random forests, subsampling and the random feature selectionmechanism, are seen to each distinctively contribute to achieving nearlyoptimal performance for the model class considered.

On the Pointwise Behavior of Recursive Partitioning and Its Implications for Heterogeneous Causal Effect Estimation