{
  "abstract": "Modern interventions increasingly produce object-valued outcomes, such as distributions, covariance matrices, networks, and trees. Existing causal frameworks often exploit special geometry such as one-dimensional Wasserstein quantiles or geodesic Fréchet means, whereas metric statistics studies random objects without confounding adjustment. We propose the profile causal effect $Δ(ω,t)$, which describes where and at what scale a treatment shifts probability mass, including changes in dispersion, tails, or structure that leave mean-level summaries unchanged. Formally, $Δ(ω,t)=\\Pr\\{d(ω,Y(1))\\le t\\}-\\Pr\\{d(ω,Y(0))\\le t\\}$ contrasts the potential-outcome probabilities of the same anchor-centered metric ball and requires no structure beyond the metric. On grids fixed by a deterministic or auxiliary design, we combine cross-fitted doubly robust scores with high-dimensional Gaussian approximation and the multiplier bootstrap to obtain simultaneous confidence bands and a global test under regularity conditions. The bands bound treatment-induced changes in ball and shell probabilities simultaneously and, at fixed anchors, extend to all radii. A protocol guides the choice of anchors and radii. Across the experiments, the global test detects concentration effects that mean-quantile and Fréchet-mean summaries miss. Its empirical size is near or below the nominal level, even under confounding, where naive metric tests are substantially oversized.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33491",
  "author_total": 2,
  "authors": [
    {
      "name": "Zheye Song"
    },
    {
      "name": "Zhiheng Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4jk2tg2t17jsv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33491",
  "fulltext_url": null,
  "id": "4jk2tg2t17jsv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33491",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "2613|Advanced Causal Inference Techniques"
    ]
  ],
  "openalex": "W7224000224",
  "pdf_url": "https://arxiv.org/pdf/2610.33491",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4jk2tg2t17jsv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:49Z",
      "native_id": "2610.33491",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33491"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Causal Inference in Metric Spaces via Distance Profiles",
  "title_text": "Causal Inference in Metric Spaces via Distance Profiles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:49Z",
  "url": "https://research.draconitic.com/paper/4jk2tg2t17jsv",
  "venue": "arXiv",
  "versions": []
}