{
  "abstract": "In this paper, we consider the problem of seriation of a permuted structured matrix based on noisy observations. The entries of the matrix relate to an expected quantification of interaction between two objects: the higher the value, the closer the objects. A popular structured class for modeling such matrices is the permuted Robinson class, namely the set of matrices whose coefficients are decreasing away from its diagonal, up to a permutation of its rows and columns. We consider in this paper two submodels of Robinson matrices: the Tœplitz model, and the latent position model. We provide a computational lower bound based on the low-degree paradigm, which hints that there is a statistical-computational gap for seriation when measuring the error based on the Frobenius norm. We also provide a simple and polynomial-time algorithm that achieves this lower bound. Along the way, we also characterize the information-theory optimal risk thereby giving evidence for the extent of the computation/information gap for this problem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "name": "Clément Berenfeld"
    },
    {
      "name": "Alexandra Carpentier"
    },
    {
      "name": "Nicolas Verzelen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7m998amfnwght.bib",
  "cited_by": 0,
  "doi": "10.3150/25-bej1915",
  "fulltext_url": null,
  "id": "7m998amfnwght",
  "issns": [
    "1350-7265"
  ],
  "landing_url": "https://hal.inrae.fr/hal-05715863v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.stat"
    ],
    [
      "openalex",
      "2613|Statistical Methods and Inference"
    ]
  ],
  "openalex": "W7172014247",
  "pdf_url": "https://hal.inrae.fr/hal-05715863/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": "Bernoulli Society for Mathematical Statistics and Probability",
  "ris": "https://research.draconitic.com/paper/7m998amfnwght.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:59Z",
      "native_id": "hal-05715863",
      "source": "hal",
      "url": "https://hal.inrae.fr/hal-05715863v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.stat",
      "subfield": "statistics"
    }
  ],
  "title": "Seriation of Tœplitz and latent position matrices: Optimal rates and computational trade-offs",
  "title_text": "Seriation of Tœplitz and latent position matrices: Optimal rates and computational trade-offs",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:59Z",
  "url": "https://research.draconitic.com/paper/7m998amfnwght",
  "venue": "Bernoulli",
  "versions": []
}