# Variable importance for causal forests: breaking down the heterogeneity of treatment effects

arXiv: https://arxiv.org/abs/2308.03369 · HTML: https://mlsanity.com/paper/2308.03369/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 34 references that are in the map.
- First posted on arXiv 7 Aug 2023.

## Builds on (most cited first, 13 of 13)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [Unrestricted Permutation forces Extrapolation: Variable Importance Requires at least One More Model, or There Is No Free Variable Importance](https://mlsanity.com/paper/1905.03151/) (2019)
- [Consistency of random forests](https://mlsanity.com/paper/1405.2881/) (2014)
- [Estimating Treatment Effects with Causal Forests: An Application](https://mlsanity.com/paper/1902.07409/) (2019)
- [A general framework for inference on algorithm-agnostic variable importance](https://mlsanity.com/paper/2004.03683/) (2020)
- [MDA for random forests: inconsistency, and a practical solution via the Sobol-MDA](https://mlsanity.com/paper/2102.13347/) (2021)
- [Variable importance measures for heterogeneous treatment effects](https://mlsanity.com/paper/2204.06030/) (2022)
- [Risk ratio, odds ratio, risk difference... Which causal measure is easier to generalize?](https://mlsanity.com/paper/2303.16008/) (2023)
- [A Flexible Approach for Predictive Biomarker Discovery](https://mlsanity.com/paper/2205.01285/) (2022)

## Built on by (most cited first, 6 of 6)

- [Measuring Variable Importance in Heterogeneous Treatment Effects with Confidence](https://mlsanity.com/paper/2408.13002/) (2024)
- [Transparency challenges in policy evaluation with causal machine learning -- improving usability and accountability](https://mlsanity.com/paper/2310.13240/) (2023)
- [Inference on Variable Importance for Treatment Effect Heterogeneity: Shapley Values and Beyond](https://mlsanity.com/paper/2510.18843/) (2025)
- [Distilling interpretable causal trees from causal forests](https://mlsanity.com/paper/2408.01023/) (2024)
- [ConfoundingSHAP: Quantifying confounding strength in causal inference](https://mlsanity.com/paper/2605.10533/) (2026)
- [Splitting the Difference: Interpretable Causal Forests for Treatment Effect Heterogeneity and Bias](https://mlsanity.com/paper/2609.16971/) (2026)

## Abstract (arXiv)

Causal random forests provide efficient estimates of heterogeneous treatment effects. However, forest algorithms are also well-known for their black-box nature, and therefore, do not characterize how input variables are involved in treatment effect heterogeneity, which is a strong practical limitation. In this article, we develop a new importance variable algorithm for causal forests, to quantify the impact of each input on the heterogeneity of treatment effects. The proposed approach is inspired from the drop and relearn principle, widely used for regression problems. Importantly, we show how to handle the forest retrain without a confounding variable. If the confounder is not involved in the treatment effect heterogeneity, the local centering step enforces consistency of the importance measure. Otherwise, when a confounder also impacts heterogeneity, we introduce a corrective term in the retrained causal forest to recover consistency. Additionally, experiments on simulated, semi-synthetic, and real data show the good performance of our importance measure, which outperforms competitors on several test cases. Experiments also show that our approach can be efficiently extended to groups of variables, providing key insights in practice.