{
  "abstract": "We present a method for recovering the moral graph of a causal DAG from a probability distribution over discrete variables, using fully connected tensor networks (FCTNs) with nuclear-norm-regularized bond corrections. Each bond matrix is parameterized as a baseline all-ones matrix plus a low-rank correction $C_{ij} = U_{ij}V_{ij}^\\top$, and the nuclear norm of the correction implemented via the variational Frobenius norm penalty on the factors drives unnecessary bonds to zero. We prove that under faithfulness, positivity, and a no-implicit-rerouting assumption on the local tensor architecture, \\textbf{every} optimal FCTN with zero reconstruction error $\\varepsilon = 0$ has effective graph exactly equal to the moral graph. For the approximate regime ($\\varepsilon > 0$), we provide explicit recovery bounds using the Fannes-Audenaert continuity of conditional mutual information, and derive a sufficient condition on the regularization parameter $β$. The effective graph is read directly from the optimized bond matrices.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09258",
  "author_total": 5,
  "authors": [
    {
      "name": "Á. Troyano Olivas"
    },
    {
      "name": "Chi-Hang Fred Fung"
    },
    {
      "name": "Hans H. Brunner"
    },
    {
      "name": "Momtchil Peev"
    },
    {
      "name": "Vicente Martin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8gt48v27haf7x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09258",
  "fulltext_url": null,
  "id": "8gt48v27haf7x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09258",
  "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.IT"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Bayesian Modeling and Causal Inference"
    ]
  ],
  "openalex": "W7212192118",
  "pdf_url": "https://arxiv.org/pdf/2609.09258",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8gt48v27haf7x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:12Z",
      "native_id": "2609.09258",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09258"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Tensor Network Moral Graph Recovery of Discrete Probability Distributions",
  "title_text": "Tensor Network Moral Graph Recovery of Discrete Probability Distributions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:22Z",
  "url": "https://research.draconitic.com/paper/8gt48v27haf7x",
  "venue": "arXiv",
  "versions": []
}