{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35898",
  "author_total": 1,
  "authors": [
    {
      "name": "Hugo Gobato Souto"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/41vpqyjxe3t6j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35898",
  "fulltext_url": null,
  "id": "41vpqyjxe3t6j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35898",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.35898",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/41vpqyjxe3t6j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:41Z",
      "native_id": "2609.35898",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35898"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Wasserstein Causal Forests for Distribution-Valued Outcomes",
  "title_text": "Wasserstein Causal Forests for Distribution-Valued Outcomes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:41Z",
  "url": "https://research.draconitic.com/paper/41vpqyjxe3t6j",
  "venue": "arXiv",
  "versions": []
}