{
  "abstract": "We introduce statistical theory for the matching of finitely many objects, represented as metric measure spaces (mm-spaces). The approach is based on the second lower bound (SLB) of the Gromov-Wasserstein distance and thus is able to identify deviations in the distributions of the (pairwise) distances within each mm-space. We introduce a surrogate of the SLB barycenter which can be easily computed and expressed explicitly in terms of the distance distributions of each object. When comparing $m$ mm-spaces for $n$ randomly drawn samples in each space, the resulting statistic then can be calculated efficiently in $O(m \\cdot n^2 \\log(n))$ basic operations. We derive the asymptotic distribution and finite-sample bounds of the proposed test statistic, which serves as a basis for a variety of tools for statistical inference, specifically an asymptotic test for pose-invariant object discrimination and a classification method (based on the SLB barycenter) with controlled error rates. These methods are investigated in simulations and applied to the structural comparison of protein domains.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11670",
  "author_total": 4,
  "authors": [
    {
      "name": "Florian Steinkamp"
    },
    {
      "name": "Luis-Alberto Rodríguez"
    },
    {
      "name": "Jan Victor Otte"
    },
    {
      "name": "Axel Munk"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1rhmavwe35t3p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11670",
  "fulltext_url": null,
  "id": "1rhmavwe35t3p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11670",
  "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",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7212280041",
  "pdf_url": "https://arxiv.org/pdf/2609.11670",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1rhmavwe35t3p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11670",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11670"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Gromov-Wasserstein Barycenter Surrogates: Statistical Methodology, Distributional Limits and Applications",
  "title_text": "Gromov-Wasserstein Barycenter Surrogates: Statistical Methodology, Distributional Limits and Applications",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:36Z",
  "url": "https://research.draconitic.com/paper/1rhmavwe35t3p",
  "venue": "arXiv",
  "versions": []
}