Wasserstein Causal Forests for Distribution-Valued Outcomes
Abstract
This paper proposes Wasserstein Causal Forests (WCF) for settings in which each unit's outcome is itself a probability distribution. This study also defines finite-grid transformed average and conditional average treatment effects, including a reference-distance contrast that asks whether treatment moves unit-level distributions toward a prespecified benchmark. Simulations cover null effects, location and shape changes, limited overlap, equal-mean but different laws, heterogeneous effects, multimodality, and structural zeros. WCF is most accurate on the conditional-law metric in most reported designs and sharply improves reference-effect estimation in the principal location-and-shape settings, but it is less accurate than the forest baselines for multimodal settings. WCF is applied to the famous Project STAR \citep{word1990state}, revealing that small classes alter more than the mean: they raise within-grade mathematics achievement by $0.161$ standard deviations on average (SE $0.028$); but the gain is not a uniform location shift, it is larger in the upper part of the classroom score distribution (+0.179 at the ninetieth percentile versus +0.091 at the tenth) and, in descriptive stratum estimates, largest in the schools serving the most economically disadvantaged students (highest free-lunch quartile, +0.262, versus +0.092 to +0.164 elsewhere), while overall dispersion is essentially unchanged.
Related
- Exhaustive adjustment-set selection and causal effects for distribution-valued outcomes, with inference under latent Gaussian spatio-temporal dependence
- Wasserstein Kernel Regression with Dependent Distribution-Valued Predictors: Local Recurrence, Joint Inference, and Multivariate Gaussian Geometry
- Factorial Multivariate Bayesian Causal Forests: heterogeneous main and interaction effects of multiple treatments on correlated outcomes
- Bayesian Causal Forests for Zero-Inflated Continuous Outcomes
- Continuity equation on metric spaces via measure-valued derivations and BV-Wasserstein curves
BibTeX
@misc{souto2026wasserstein,
title = {{Wasserstein Causal Forests for Distribution-Valued Outcomes}},
author = {Hugo Gobato Souto},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35898},
eprint = {2609.35898},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35898},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Wasserstein Causal Forests for Distribution-Valued Outcomes
AU - Hugo Gobato Souto
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.35898
UR - https://arxiv.org/abs/2609.35898
AB - This paper proposes Wasserstein Causal Forests (WCF) for settings in which each unit's outcome is itself a probability distribution. This study also defines finite-grid transformed average and conditional average treatment effects, including a reference-distance contrast that asks whether treatment moves unit-level distributions toward a prespecified benchmark. Simulations cover null effects, location and shape changes, limited overlap, equal-mean but different laws, heterogeneous effects, multimodality, and structural zeros. WCF is most accurate on the conditional-law metric in most reported designs and sharply improves reference-effect estimation in the principal location-and-shape settings, but it is less accurate than the forest baselines for multimodal settings. WCF is applied to the famous Project STAR \citep{word1990state}, revealing that small classes alter more than the mean: they raise within-grade mathematics achievement by $0.161$ standard deviations on average (SE $0.028$); but the gain is not a uniform location shift, it is larger in the upper part of the classroom score distribution (+0.179 at the ninetieth percentile versus +0.091 at the tenth) and, in descriptive stratum estimates, largest in the schools serving the most economically disadvantaged students (highest free-lunch quartile, +0.262, versus +0.092 to +0.164 elsewhere), while overall dispersion is essentially unchanged.
ER -