Wasserstein Causal Forests for Distribution-Valued Outcomes

arXiv:2609.35898v1 Announce Type: cross 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 itep{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

• Robust Chance-Constrained Optimization using a Continuous Parameter Space Wasserstein-2 Ambiguity Set of Gaussian Mixtures
• Sharper Bounds for Chebyshev Moment Matching, with Applications
• Tensor Network Moral Graph Recovery of Discrete Probability Distributions

Source: arXiv cs.LG | 2026-09-30