# Inference on Variable Importance for Treatment Effect Heterogeneity: Shapley Values and Beyond

arXiv: https://arxiv.org/abs/2510.18843 · HTML: https://mlsanity.com/paper/2510.18843/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 59 references that are in the map.
- First posted on arXiv 21 Oct 2025.

## Builds on (most cited first, 26 of 26)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [ranger: A Fast Implementation of Random Forests for High Dimensional Data in C++ and R](https://mlsanity.com/paper/1508.04409/) (2015)
- [Sampling Permutations for Shapley Value Estimation](https://mlsanity.com/paper/2104.12199/) (2021)
- [A Measure-Theoretic Approach to Kernel Conditional Mean Embeddings](https://mlsanity.com/paper/2002.03689/) (2020)
- [Nonparametric methods for doubly robust estimation of continuous treatment effects](https://mlsanity.com/paper/1507.00747/) (2015)
- [Efficient nonparametric statistical inference on population feature importance using Shapley values](https://mlsanity.com/paper/2006.09481/) (2020)
- [A general framework for inference on algorithm-agnostic variable importance](https://mlsanity.com/paper/2004.03683/) (2020)
- [Conditional Distributional Treatment Effect with Kernel Conditional Mean Embeddings and U-Statistic Regression](https://mlsanity.com/paper/2102.08208/) (2021)
- [Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations](https://mlsanity.com/paper/2207.06503/) (2022)
- [Feature Importance: A Closer Look at Shapley Values and LOCO](https://mlsanity.com/paper/2303.05981/) (2023)
- [Counterfactual Predictions under Runtime Confounding](https://mlsanity.com/paper/2006.16916/) (2020)
- [One-Step Estimation of Differentiable Hilbert-Valued Parameters](https://mlsanity.com/paper/2303.16711/) (2023)
- [On Weighted Orthogonal Learners for Heterogeneous Treatment Effects](https://mlsanity.com/paper/2303.12687/) (2023)
- [Simplifying debiased inference via automatic differentiation and probabilistic programming](https://mlsanity.com/paper/2405.08675/) (2024)
- [An Omnibus Nonparametric Test of Equality in Distribution for Unknown Functions](https://mlsanity.com/paper/1510.04195/) (2015)
- [Variable importance for causal forests: breaking down the heterogeneity of treatment effects](https://mlsanity.com/paper/2308.03369/) (2023)
- [Variable importance measures for heterogeneous treatment effects with survival outcome](https://mlsanity.com/paper/2412.11790/) (2024)
- [Inference on function-valued parameters using a restricted score test](https://mlsanity.com/paper/2105.06646/) (2021)
- [A nonparametric framework for treatment effect modifier discovery in high dimensions](https://mlsanity.com/paper/2304.05323/) (2023)
- [Targeted Learning on Variable Importance Measure for Heterogeneous Treatment Effect](https://mlsanity.com/paper/2309.13324/) (2023)
- [Nonparametric inference on non-negative dissimilarity measures at the boundary of the parameter space](https://mlsanity.com/paper/2306.07492/) (2023)
- [An Approach to Nonparametric Inference on the Causal Dose Response Function](https://mlsanity.com/paper/2306.07736/) (2023)

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

- [Statistical Inference and Learning for Shapley Additive Explanations (SHAP)](https://mlsanity.com/paper/2602.10532/) (2026)
- [Semiparametrically Efficient Inference for Kernel Measures of Noise Heterogeneity](https://mlsanity.com/paper/2605.27526/) (2026)

## Abstract (arXiv)

We provide an inferential framework to assess variable importance for heterogeneous treatment effects. This assessment is especially useful in high-risk domains such as medicine, where decision makers hesitate to rely on black-box treatment recommendation algorithms. The variable importance measures we consider are local in that they may differ across individuals, while the inference is global in that it tests whether a given variable is important for any individual. Our approach builds on recent developments in semiparametric theory for function-valued parameters, and is valid even when statistical machine learning algorithms are employed to quantify treatment effect heterogeneity. We demonstrate the applicability of our method to infectious disease prevention strategies.