{
  "abstract": "Variance-based methods recover a Gaussian linear structural equation model (SEM) with equal or suitably constrained error variances, either by recursively identifying the source nodes with smallest conditional variance (top-down method) or sink nodes with highest conditional variance (bottom-up method). We show that the use of conditional variance is incidental: replacing it with the conditional risk, i.e., the minimal expected loss of linear prediction under the negative log-likelihood of the noise distribution, extends both methods to non-Gaussian noise. Existing methods are the least-squares special case. This yields two main results. First, exploiting the noise distribution improves structure recovery: the matched-loss procedures recover the SEM more accurately than their least-squares counterparts and the LiNGAM methods, which are designed for non-Gaussianity. Second, the two methods, interchangeable in the Gaussian setting, separate under non-Gaussian noise: the top-down method is correct for every noise density with finite differential entropy, whereas the bottom-up method requires a regularity condition and can fail without it, for instance under mean-zero exponential or Cauchy noise. Simulations confirm both results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14246",
  "author_total": 3,
  "authors": [
    {
      "name": "Ujas Shah"
    },
    {
      "name": "Panagiota Birmpa"
    },
    {
      "name": "Rebecca Morrison"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c5hmvxy1tyjy3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14246",
  "fulltext_url": null,
  "id": "c5hmvxy1tyjy3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14246",
  "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",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Bayesian Modeling and Causal Inference"
    ]
  ],
  "openalex": "W7221746653",
  "pdf_url": "https://arxiv.org/pdf/2610.14246",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c5hmvxy1tyjy3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:26Z",
      "native_id": "2610.14246",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14246"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Learning Non-Gaussian SEMs with Conditional Risk, and Why the Direction of Recursion Matters",
  "title_text": "Learning Non-Gaussian SEMs with Conditional Risk, and Why the Direction of Recursion Matters",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:26Z",
  "url": "https://research.draconitic.com/paper/c5hmvxy1tyjy3",
  "venue": "arXiv",
  "versions": []
}