{
  "abstract": "What determines the unavoidable sample cost of learning cyclic causal structure? For cyclic linear non-Gaussian models, we study exact condensation recovery from observational data: identifying the strongly connected component (SCC) partition and all edges between components. We establish the first information-theoretic lower bounds on sample complexity for this target. For $p$ variables, maximum SCC size $s_{\\max}$, and maximum external-parent count $d_B$, any estimator requires order $s_{\\max}\\log(ep/s_{\\max})+d_B\\log(ep/d_B)$ samples in the worst case over a regular model class. These bounds distinguish the costs of SCC membership and external-parent selection. Under principal invertibility and without correlation faithfulness, we establish a population block-exogeneity principle that identifies unknown root SCCs through residual independence and inclusion minimality. A sparse-adjustment characterization shows that small adjustment sets suffice to identify SCCs and their direct external parents, without regressing on all previously recovered variables. These characterizations yield BlockExo, which attains a structurally matching sample bound without knowing $s_{\\max}$ or $d_B$ under suitable conditions. Simulations support the structural dependence of our sample bound and demonstrate BlockExo's sample-efficient recovery in comparisons with other methods for cyclic causal discovery.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.34050",
  "author_total": 3,
  "authors": [
    {
      "name": "Sunmin Oh"
    },
    {
      "name": "Seungsu Han"
    },
    {
      "name": "Gunwoong Park"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3nj3f33974wwj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.34050",
  "fulltext_url": null,
  "id": "3nj3f33974wwj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.34050",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Bayesian Modeling and Causal Inference"
    ]
  ],
  "openalex": "W7214784075",
  "pdf_url": "https://arxiv.org/pdf/2609.34050",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3nj3f33974wwj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:26Z",
      "native_id": "2609.34050",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.34050"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "The Statistical Cost of Causal Discovery with Feedback",
  "title_text": "The Statistical Cost of Causal Discovery with Feedback",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:26Z",
  "url": "https://research.draconitic.com/paper/3nj3f33974wwj",
  "venue": "arXiv",
  "versions": []
}