{
  "abstract": "As part of the study of an input-output numerical simulator, performing a sensitivity analysis allows to identify the input parameters having the greatest influence on the output variability. Since the variance-based approach (also known as the ANOVA framework) is too expensive, and the kernel-based approach (leading to HSIC indices) lacks interpretability, the HSIC-ANOVA framework has recently emerged to marry the advantages of both. A major particularity of this new methodology is the need to use the unanchored Sobolev kernels. This paper investigates how sensitivity is measured according to the chosen Sobolev kernel. To achieve this, at least one explicit feature map is extracted from each Sobolev kernel and this helps identify the dependence patterns captured by HSIC-ANOVA indices. For the Sobolev kernel of order r = 1, three different proof techniques are proposed to disclose its Mercer feature map. For higher-order Sobolev kernels (r ≥ 2), it is proved that the Mercer feature map does not have a closed-form expression. In response, a slightly relaxed feature map is obtained after considering a sub-kernel decomposition. This latter feature map allows to justify why the Sobolev kernels of order r ≥ 2 should not be used to estimate HSIC-ANOVA indices.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "name": "Gabriel Sarazin"
    },
    {
      "name": "Amandine Marrel"
    },
    {
      "name": "Sebastien da Veiga"
    },
    {
      "name": "Vincent Chabridon"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/20xpwca54mad9.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "20xpwca54mad9",
  "issns": [],
  "landing_url": "https://cea.hal.science/cea-04320711v2",
  "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.math"
    ],
    [
      "hal",
      "0.stat"
    ],
    [
      "hal",
      "1.math.math-ap"
    ],
    [
      "hal",
      "1.math.math-st"
    ],
    [
      "hal",
      "1.stat.th"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://cea.hal.science/cea-04320711/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/20xpwca54mad9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:56Z",
      "native_id": "cea-04320711",
      "source": "hal",
      "url": "https://cea.hal.science/cea-04320711v2"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-ap",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "hal:0.stat",
      "subfield": "statistics"
    }
  ],
  "title": "New insights into the feature maps of Sobolev kernels: application in global sensitivity analysis",
  "title_text": "New insights into the feature maps of Sobolev kernels: application in global sensitivity analysis",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:56Z",
  "url": "https://research.draconitic.com/paper/20xpwca54mad9",
  "venue": "HAL",
  "versions": []
}