# CURLS: Causal Rule Learning for Subgroups with Significant Treatment Effect

arXiv: https://arxiv.org/abs/2407.01004 · HTML: https://mlsanity.com/paper/2407.01004/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 64 references that are in the map.
- First posted on arXiv 1 Jul 2024.

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

- [Neural Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1611.09940/) (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)
- [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)
- [Boolean Decision Rules via Column Generation](https://mlsanity.com/paper/1805.09901/) (2018)
- [Estimating Treatment Effects with Causal Forests: An Application](https://mlsanity.com/paper/1902.07409/) (2019)
- [A Survey of Learning Causality with Data: Problems and Methods](https://mlsanity.com/paper/1809.09337/) (2018)
- [Machine Learning Estimation of Heterogeneous Treatment Effects with Instruments](https://mlsanity.com/paper/1905.10176/) (2019)
- [Causal Rule Sets for Identifying Subgroups with Enhanced Treatment Effect](https://mlsanity.com/paper/1710.05426/) (2017)
- [Diverse Rule Sets](https://mlsanity.com/paper/2006.09890/) (2020)
- [LIBRE: Learning Interpretable Boolean Rule Ensembles](https://mlsanity.com/paper/1911.06537/) (2019)
- [From Observational Studies to Causal Rule Mining](https://mlsanity.com/paper/1508.03819/) (2015)

## Built on by (most cited first, 2 of 2)

- [MOSIC: Model-Agnostic Optimal Subgroup Identification with Multi-Constraint for Improved Reliability](https://mlsanity.com/paper/2504.20908/) (2025)
- [Can Broad Biomedical Knowledge be Contextualized into Scenario-Grounded Propositions?](https://mlsanity.com/paper/2605.27082/) (2026)

## Abstract (arXiv)

In causal inference, estimating heterogeneous treatment effects (HTE) is critical for identifying how different subgroups respond to interventions, with broad applications in fields such as precision medicine and personalized advertising. Although HTE estimation methods aim to improve accuracy, how to provide explicit subgroup descriptions remains unclear, hindering data interpretation and strategic intervention management. In this paper, we propose CURLS, a novel rule learning method leveraging HTE, which can effectively describe subgroups with significant treatment effects. Specifically, we frame causal rule learning as a discrete optimization problem, finely balancing treatment effect with variance and considering the rule interpretability. We design an iterative procedure based on the minorize-maximization algorithm and solve a submodular lower bound as an approximation for the original. Quantitative experiments and qualitative case studies verify that compared with state-of-the-art methods, CURLS can find subgroups where the estimated and true effects are 16.1% and 13.8% higher and the variance is 12.0% smaller, while maintaining similar or better estimation accuracy and rule interpretability. Code is available at https://osf.io/zwp2k/.