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

TL;DR

This paper critically examines the limitations of recursive partitioning decision trees for pointwise inference in causal effect estimation, highlighting their slow convergence and proposing random forests as a remedy for improved performance.

Contribution

It demonstrates the potential failure of adaptive decision trees in uniform norm convergence and shows how random forests can nearly achieve optimal rates, despite added complexity.

Findings

Decision trees can fail to achieve polynomial convergence rates in uniform norm.

Random forests improve convergence rates, approaching optimal performance.

Subsampling and random feature selection are key to the success of random forests.

Abstract

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.