{
  "abstract": "We present a unified framework for uncertainty quantification over filtration scale, extending the topological average treatment effect (TATE) analysis of \\citet{kim-lee} to conditional mean confidence and individual effect prediction. For the conditional topological average treatment effect (CTATE), we derive multiplier confidence bands at a fixed covariate value, simultaneous over filtration scale, and prove validity in a correctly specified finite-dimensional regression regime, with explicit control of smoothing bias and nuisance-estimation error. For the individual topological treatment effect (ITTE), we integrate existing weighted and functional split-conformal methods to obtain finite-sample marginal prediction coverage under known target-to-calibration likelihood ratios, with a total-variation bound for estimated ratios. We also extend the current TATE silhouette stability analysis to the diagram-independent bound $\\|Φ_r(D)-Φ_r(D')\\|_\\infty \\le (1+2r)W_1(D,D')$ for $r\\geq1$, recovering the known $r=1$ constant, and propagate diagram approximation error to prediction bands. The installable Python library \\texttt{tcda\\_uq} integrates mean confidence, individual prediction, and topological preprocessing, with tutorials and reproduction materials. Simulations and a PACCE lesion-measurement application illustrate the distinct coverage targets and the importance of declaring the target population.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41593",
  "author_total": 2,
  "authors": [
    {
      "name": "Hugo G. Souto"
    },
    {
      "name": "Ioannis Diamantis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b5b4ksxxk8dye.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41593",
  "fulltext_url": null,
  "id": "b5b4ksxxk8dye",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41593",
  "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",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.TH"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41593",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b5b4ksxxk8dye.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41593",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41593"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Uncertainty Quantification for Topological Treatment Effects",
  "title_text": "Uncertainty Quantification for Topological Treatment Effects",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:53Z",
  "url": "https://research.draconitic.com/paper/b5b4ksxxk8dye",
  "venue": "arXiv",
  "versions": []
}