# Causal Rule Ensemble: Interpretable Discovery and Inference of Heterogeneous Treatment Effects

arXiv: https://arxiv.org/abs/2009.09036 · HTML: https://mlsanity.com/paper/2009.09036/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Sep 2020.

## Built on by (most cited first, 13 of 13)

- [Exploratory Causal Inference in SAEnce](https://mlsanity.com/paper/2510.14073/) (2025)
- [A New Causal Rule Learning Approach to Interpretable Estimation of Heterogeneous Treatment Effect](https://mlsanity.com/paper/2310.06746/) (2023)
- [Towards Stable Machine Learning Model Retraining via Slowly Varying Sequences](https://mlsanity.com/paper/2403.19871/) (2024)
- [CausalKANs: interpretable treatment effect estimation with Kolmogorov-Arnold networks](https://mlsanity.com/paper/2509.22467/) (2025)
- [Causal Clustering for Conditional Average Treatment Effects Estimation and Subgroup Discovery](https://mlsanity.com/paper/2509.05775/) (2025)
- [Enhancing Medical Learning and Reasoning Systems: A Boxology-Based Comparative Analysis of Design Patterns](https://mlsanity.com/paper/2408.02709/) (2024)
- [Causal Rule Forest: Toward Interpretable and Precise Treatment Effect Estimation](https://mlsanity.com/paper/2408.15055/) (2024)
- [Towards Optimal Environmental Policies: Policy Learning under Arbitrary Bipartite Network Interference](https://mlsanity.com/paper/2410.08362/) (2024)
- [Causal rule ensemble approach for multi-arm data](https://mlsanity.com/paper/2504.17166/) (2025)
- [Moment Matters: Mean and Variance Causal Graph Discovery from Heteroscedastic Observational Data](https://mlsanity.com/paper/2602.23602/) (2026)
- [Fast Uncertainty Quantification for Kernel-Based Estimators in Large-Scale Causal Inference](https://mlsanity.com/paper/2603.13662/) (2026)
- [Kolmogorov-Arnold causal generative models](https://mlsanity.com/paper/2603.20184/) (2026)
- [From Tokens to Policy: Causal and Interpretable Heterogeneous Treatment Effects Identification](https://mlsanity.com/paper/2606.17010/) (2026)

## Abstract (arXiv)

In health and social sciences, it is critically important to identify subgroups of the study population where there is notable heterogeneity of treatment effects (HTE) with respect to the population average. Decision trees have been proposed and commonly adopted for the data-driven discovery of HTE due to their high level of interpretability. However, single-tree discovery of HTE can be unstable and oversimplified. This paper introduces the Causal Rule Ensemble (CRE), a new method for HTE discovery and estimation using an ensemble-of-trees approach. CRE offers several key features, including 1) an interpretable representation of the HTE; 2) the ability to explore complex heterogeneity patterns; and 3) high stability in subgroups discovery. The discovered subgroups are defined in terms of interpretable decision rules. Estimation of subgroup-specific causal effects is performed via a two-stage approach, for which we provide theoretical guarantees. Through simulations, we show that the CRE method is highly competitive compared to state-of-the-art techniques. Finally, we apply CRE to discover the heterogeneous health effects of exposure to air pollution on mortality for 35.3 million Medicare beneficiaries across the contiguous U.S.