{
  "abstract": "Conditional sampling is central to Bayesian inference, generative modeling, and causal inference: given a joint law for random variables $X$ and $Y$ and an observation $Y=y$, one seeks to sample from the conditional law of $X\\mid Y=y$. Even when the joint distribution is accurately represented, this task can be computationally difficult as it may require evaluating intractable normalizing constants or solving a new inference problem for each observation. Measure transport provides an approach to this problem by identifying a map with triangular structure that directly pushes forward a reference to the conditional of a joint distribution for any observation. This article reviews the theoretical, methodological, and algorithmic foundations of triangular transports, with the Knothe-Rosenblatt rearrangement as a canonical construction. We discuss methods for estimating triangular maps from finite samples, as well as their use in simulation-based inference and causal inference. While our primary aim is to review existing formulations, we also present new ideas and open questions for conditional sampling using transport.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01436",
  "author_total": 3,
  "authors": [
    {
      "name": "Ricardo Baptista"
    },
    {
      "name": "Benjamin Bloem-Reddy"
    },
    {
      "name": "Bamdad Hosseini"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0rmamaag72z21.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01436",
  "fulltext_url": null,
  "id": "0rmamaag72z21",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01436",
  "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",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "arxiv",
      "stat.TH"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01436",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0rmamaag72z21.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01436",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01436"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Transport for Conditional Sampling: Foundations and Applications",
  "title_text": "Transport for Conditional Sampling: Foundations and Applications",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:35Z",
  "url": "https://research.draconitic.com/paper/0rmamaag72z21",
  "venue": "arXiv",
  "versions": []
}