Explaining Heterogeneous Treatment Effects with Causal Forests and the Hoeffding Functional Decomposition
Abstract
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.
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BibTeX
@misc{patinier2026explaining,
title = {{Explaining Heterogeneous Treatment Effects with Causal Forests and the Hoeffding Functional Decomposition}},
author = {Gaëtan Patinier and Clément Bénard and Margaux Törnqvist},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16447},
eprint = {2610.16447},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05786424v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Explaining Heterogeneous Treatment Effects with Causal Forests and the Hoeffding Functional Decomposition
AU - Gaëtan Patinier
AU - Clément Bénard
AU - Margaux Törnqvist
PY - 2026
DA - 2026/10/09
PB - HAL
DO - 10.48550/arxiv.2610.16447
UR - https://hal.science/hal-05786424v1
AB - 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.
ER -