# Explaining Heterogeneous Treatment Effects with Causal Forests and the Hoeffding Functional Decomposition

arXiv: https://arxiv.org/abs/2610.16447 · HTML: https://mlsanity.com/paper/2610.16447/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 26 references that are in the map.
- First posted on arXiv 12 Oct 2026.

## Builds on (most cited first, 12 of 12)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [Generalized Random Forests](https://mlsanity.com/paper/1610.01271/) (2016)
- [Consistency of random forests](https://mlsanity.com/paper/1405.2881/) (2014)
- [From Shapley Values to Generalized Additive Models and back](https://mlsanity.com/paper/2209.04012/) (2022)
- [Purifying Interaction Effects with the Functional ANOVA: An Efficient Algorithm for Recovering Identifiable Additive Models](https://mlsanity.com/paper/1911.04974/) (2019)
- [Beyond TreeSHAP: Efficient Computation of Any-Order Shapley Interactions for Tree Ensembles](https://mlsanity.com/paper/2401.12069/) (2024)
- [Linear TreeShap](https://mlsanity.com/paper/2209.08192/) (2022)
- [Tree Ensemble Explainability through the Hoeffding Functional Decomposition and TreeHFD Algorithm](https://mlsanity.com/paper/2510.24815/) (2025)
- [Variable importance measures for heterogeneous treatment effects with survival outcome](https://mlsanity.com/paper/2412.11790/) (2024)

## Abstract (arXiv)

The estimation of heterogeneous treatment effects is a central objective of causal inference. However, state-of-the-art algorithms to solve this task are based on machine learning principles, and thus behave as black boxes. Consequently, the identification of covariates driving heterogeneity remains a challenging and open problem. To address this limitation, we introduce CausalTreeHFD, an interpretable extension of causal forests, based on the Hoeffding functional decomposition adapted to tree ensembles. Our approach decomposes predictions of conditional average treatment effects (CATE) into contributions from individual covariates and pairwise interactions, providing a direct characterization of the factors driving treatment effect heterogeneity. We establish the consistency of CausalTreeHFD, which converges towards the Hoeffding decomposition of the underlying CATE function, under standard assumptions for the analysis of causal forests. Experiments on simulated and real datasets show that CausalTreeHFD accurately identifies relevant covariates and interactions, and precisely recovers their contributions to heterogeneous treatment effects.