{
  "abstract": "Bayesian structure learning of directed acyclic graphs (DAGs) is central to high-dimensional causal discovery, yet existing methods mostly assume multivariate Gaussian data, which is routinely violated by measurements displaying heavy tails, skewness, or bounded support. We address this by introducing NPN-DAG-HS, a fully Bayesian semiparametric DAG model coupling the nonparanormal family with horseshoe shrinkage on Cholesky off-diagonals via an extended-rank likelihood. This handles arbitrary unknown monotone marginal transformations without estimating them, preserving exact-zero shrinkage and conditionally conjugate posteriors for practical inference in large dimensions. Our method uses a partially collapsed Metropolis-within-Gibbs sampler that augments rank-likelihood Gaussian copies and alternates score-based DAG moves with horseshoe Gibbs updates. Theoretically, in the high-dimensional regime ($p \\to \\infty$ with $\\log p / n \\to 0$), we establish posterior contraction at the rate $\\sqrt{(s_0+p)\\log p/n}$, strong skeleton selection consistency, and a parametric Bernstein-von Mises theorem for smooth total causal-effect functionals, yielding asymptotic frequentist calibration of credible intervals. Simulations confirm our method outperforms Gaussian baselines and standard frequentist learners. Applied to an acute myeloid leukaemia dataset, it recovers a sparse, interpretable network, pruning unsupported edges declared by Gaussian analyses and illustrating the value of our semiparametric relaxation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13007",
  "author_total": 2,
  "authors": [
    {
      "name": "Samaneh Nazari"
    },
    {
      "name": "Mohammad Arashi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6y40z55z3xxfd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13007",
  "fulltext_url": null,
  "id": "6y40z55z3xxfd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13007",
  "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"
    ],
    [
      "openalex",
      "1702|Bayesian Modeling and Causal Inference"
    ]
  ],
  "openalex": "W7213213899",
  "pdf_url": "https://arxiv.org/pdf/2609.13007",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6y40z55z3xxfd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:17Z",
      "native_id": "2609.13007",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13007"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Semiparametric Bayesian structure learning of nonparanormal directed acyclic graphs with local--global shrinkage",
  "title_text": "Semiparametric Bayesian structure learning of nonparanormal directed acyclic graphs with local--global shrinkage",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:17Z",
  "url": "https://research.draconitic.com/paper/6y40z55z3xxfd",
  "venue": "arXiv",
  "versions": []
}