# Measuring Variable Importance in Heterogeneous Treatment Effects with Confidence

arXiv: https://arxiv.org/abs/2408.13002 · HTML: https://mlsanity.com/paper/2408.13002/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 46 references that are in the map.
- First posted on arXiv 23 Aug 2024.

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

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Nonparametric Estimation of Heterogeneous Treatment Effects: From Theory to Learning Algorithms](https://mlsanity.com/paper/2101.10943/) (2021)
- [Panning for Gold: Model-X Knockoffs for High-dimensional Controlled Variable Selection](https://mlsanity.com/paper/1610.02351/) (2016)
- [Causal Machine Learning for Healthcare and Precision Medicine](https://mlsanity.com/paper/2205.11402/) (2022)
- [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)
- [Feature Importance: A Closer Look at Shapley Values and LOCO](https://mlsanity.com/paper/2303.05981/) (2023)
- [Benchmarking Heterogeneous Treatment Effect Models through the Lens of Interpretability](https://mlsanity.com/paper/2206.08363/) (2022)
- [Variable importance measures for heterogeneous treatment effects](https://mlsanity.com/paper/2204.06030/) (2022)
- [Statistically Valid Variable Importance Assessment through Conditional Permutations](https://mlsanity.com/paper/2309.07593/) (2023)
- [Variable importance for causal forests: breaking down the heterogeneity of treatment effects](https://mlsanity.com/paper/2308.03369/) (2023)
- [Variable Importance in High-Dimensional Settings Requires Grouping](https://mlsanity.com/paper/2312.10858/) (2023)
- [A Conditional Randomization Test for Sparse Logistic Regression in High-Dimension](https://mlsanity.com/paper/2205.14613/) (2022)

## Built on by (most cited first, 3 of 3)

- [Aggregate Models, Not Explanations: Improving Feature Importance Estimation](https://mlsanity.com/paper/2602.11760/) (2026)
- [ConfoundingSHAP: Quantifying confounding strength in causal inference](https://mlsanity.com/paper/2605.10533/) (2026)
- [From Tokens to Policy: Causal and Interpretable Heterogeneous Treatment Effects Identification](https://mlsanity.com/paper/2606.17010/) (2026)

## Abstract (arXiv)

Causal machine learning holds promise for estimating individual treatment effects from complex data. For successful real-world applications of machine learning methods, it is of paramount importance to obtain reliable insights into which variables drive heterogeneity in the response to treatment. We propose PermuCATE, an algorithm based on the Conditional Permutation Importance (CPI) method, for statistically rigorous global variable importance assessment in the estimation of the Conditional Average Treatment Effect (CATE). Theoretical analysis of the finite sample regime and empirical studies show that PermuCATE has lower variance than the Leave-One-Covariate-Out (LOCO) reference method and provides a reliable measure of variable importance. This property increases statistical power, which is crucial for causal inference in the limited-data regime common to biomedical applications. We empirically demonstrate the benefits of PermuCATE in simulated and real-world health datasets, including settings with up to hundreds of correlated variables.