{
  "abstract": "The problem of identifiability in linear parametric models (LPMs) whose nodes follow either an ordered logit model or a regular one-parameter exponential family is evaluated. The results go beyond classical structural equation models as well as results for nodes with observations from a homogeneous family of distributions. The main result establishes that the orientation of every edge joining an ordinal node to an exponential-family node is identifiable from the joint distribution alone at every parameter value, provided the ordinal node has at least three categories and the exponential-family node at least three points of support, with no restriction on the sufficient statistic. Converses show that both requirements are necessary: the three-category requirement is binding only for affine sufficient statistics, and the three-point requirement is binding under the canonical link. The guarantee extends to orienting every such mixed ordinal-exponential family edge of a given $d$-node undirected skeleton. Numerical experiments illustrate the theoretical results by successfully separating orientations within a Markov equivalence class, which are indistinguishable by conditional independence alone.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17942",
  "author_total": 2,
  "authors": [
    {
      "name": "Sambit Mishra"
    },
    {
      "name": "Urbashi Mitra"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fe3m04tamgn1k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17942",
  "fulltext_url": null,
  "id": "fe3m04tamgn1k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17942",
  "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",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1702|Bayesian Modeling and Causal Inference"
    ]
  ],
  "openalex": "W7213511331",
  "pdf_url": "https://arxiv.org/pdf/2609.17942",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fe3m04tamgn1k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.17942",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17942"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "On the Identifiability of Mixed Ordinal and Exponential Family Causal DAGs under Linear Parametric Models",
  "title_text": "On the Identifiability of Mixed Ordinal and Exponential Family Causal DAGs under Linear Parametric Models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:10Z",
  "url": "https://research.draconitic.com/paper/fe3m04tamgn1k",
  "venue": "arXiv",
  "versions": []
}