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

arXiv: https://arxiv.org/abs/2211.10805 · HTML: https://mlsanity.com/paper/2211.10805/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 39 references that are in the map.
- First posted on arXiv 19 Nov 2022.

## Builds on (most cited first, 8 of 8)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Interpretable machine learning: definitions, methods, and applications](https://mlsanity.com/paper/1901.04592/) (2019)
- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (2015)
- [A Survey on Causal Inference](https://mlsanity.com/paper/2002.02770/) (2020)
- [Machine Learning Methods Economists Should Know About](https://mlsanity.com/paper/1903.10075/) (2019)
- [Deep Neural Networks for Estimation and Inference](https://mlsanity.com/paper/1809.09953/) (2018)
- [Randomization as Regularization: A Degrees of Freedom Explanation for Random Forest Success](https://mlsanity.com/paper/1911.00190/) (2019)
- [Convergence Rates of Oblique Regression Trees for Flexible Function Libraries](https://mlsanity.com/paper/2210.14429/) (2022)

## Built on by (most cited first, 5 of 5)

- [On the Convergence of CART under Sufficient Impurity Decrease Condition](https://mlsanity.com/paper/2310.17114/) (2023)
- [When do Random Forests work?](https://mlsanity.com/paper/2504.12860/) (2025)
- [Honesty in Causal Forests: When It Helps and When It Hurts](https://mlsanity.com/paper/2506.13107/) (2025)
- [End-Cut Preference in Survival Trees](https://mlsanity.com/paper/2509.18477/) (2025)
- [Covariance-Driven Regression Trees: Reducing Overfitting in CART](https://mlsanity.com/paper/2601.07281/) (2026)

## Abstract (arXiv)

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.