{
  "abstract": "Inferring higher-order interaction structure from observations of dynamics is a central challenge in complex systems, particularly when data are scarce, noisy, or concentrated in lower-dimensional regions of state space. We develop Bayes-THIS, a Bayesian extension of Taylor-based Hypergraph Inference using SINDy (THIS) that replaces threshold-based sparse regression with sparse Bayesian regression using automatic relevance determination. This yields adaptive, term-wise shrinkage and a posterior over inferred Taylor expansion coefficients that encode the presence or absence of interactions. Across numerical experiments, Bayes-THIS improves inference in low-data, high-noise, and ill-conditioned regimes. The Bayesian formulation also enables two capabilities absent from the original THIS framework: a posterior predictive diagnostic for assessing whether a dataset contains higher-order signal distinguishable from noise, and a posterior interval rule for pruning weakly supported hyperedges. Finally, we examine a separate, structural limitation of Taylor-based hypergraph reconstruction: higher-order interactions can produce spurious lower-order signatures that are indistinguishable from genuine lower-order edges. We find that the severity of this non-identifiability depends on cross-order support, showing that structural properties of the target hypergraph can be as important as data quality in determining what can be inferred from dynamics within this framework.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.04218",
  "author_total": 3,
  "authors": [
    {
      "name": "Katerina Tang"
    },
    {
      "name": "Vivek Srikrishnan"
    },
    {
      "name": "Jackson Kulik"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b5n5502738tyj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.04218",
  "fulltext_url": null,
  "id": "b5n5502738tyj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.04218",
  "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",
      "physics.data-an"
    ],
    [
      "arxiv",
      "physics.soc-ph"
    ],
    [
      "arxiv",
      "stat.ME"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2605.04218",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b5n5502738tyj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:48Z",
      "native_id": "2605.04218",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.04218"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.data-an",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.soc-ph",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Bayesian hypergraph inference from scarce and noisy dynamical observations",
  "title_text": "Bayesian hypergraph inference from scarce and noisy dynamical observations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:58Z",
  "url": "https://research.draconitic.com/paper/b5n5502738tyj",
  "venue": "arXiv",
  "versions": []
}