{
  "abstract": "Learning topological structure from sparsely contaminated data requires robust statistical methods, as even a small fraction of atypical observations can substantially distort the inferred topology. This article introduces a robust framework for topological learning through the Huberized Distance-to-Measure, which provides a robust filtration-generating functional for persistent homology. We establish large-sample properties of the proposed functional, and show that the associated filtration induces stable and consistent persistence diagrams. We further derive a maximum bias bound for persistence diagrams in bottleneck distance, thereby providing a quantitative measure of the sparseness associated with topological inference. The practical utility of the methodology thorough testing of statistical hypothesis problem is illustrated for a seven-circle packing configuration under sparse contamination, where it recovers the underlying topological structure. Its applicability to real data is further demonstrated through an analysis of the M-ferritin protein structure, where the method identifies a persistent $H_2$ feature corresponding to the iron-storage cavity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24170",
  "author_total": 2,
  "authors": [
    {
      "name": "Tuhin Subhra Mahato"
    },
    {
      "name": "Subhra Sankar Dhar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0gb9qh91q8r6y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24170",
  "fulltext_url": null,
  "id": "0gb9qh91q8r6y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24170",
  "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",
      "stat.ME"
    ],
    [
      "openalex",
      "1703|Topological and Geometric Data Analysis"
    ]
  ],
  "openalex": "W7223040391",
  "pdf_url": "https://arxiv.org/pdf/2610.24170",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0gb9qh91q8r6y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:33:54Z",
      "native_id": "2610.24170",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24170"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Topological Learning under Sparsity through Huberized Distance Functionals",
  "title_text": "Topological Learning under Sparsity through Huberized Distance Functionals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:54Z",
  "url": "https://research.draconitic.com/paper/0gb9qh91q8r6y",
  "venue": "arXiv",
  "versions": []
}