{
  "abstract": "Automatic relevance determination (ARD), the default tool for variable selection in Gaussian-process (GP) regression, ranks inputs by inverse lengthscales -- which measure how fast a function varies, not how much an input contributes to prediction -- and offers no calibrated rule for deciding which inputs to keep. The prediction-centred alternative, the derivative sensitivity $ν_j = \\mathbb{E}[(\\partial f/\\partial x_j)^2]$, is available in closed form from a fitted GP, but turning it into a selection rule is harder than it looks: at a null input the estimator is a degenerate quadratic form, so Wald and Bernstein-von Mises cutoffs are anti-conservative, and the natural residual bootstrap is mis-scaled. We show that a studentized multiplier bootstrap of the GP derivative process repairs both, prove its validity through an invariance principle for quadratic forms, and obtain asymptotic family-wise and false-discovery-rate control across inputs. Over 100 replications the rule controls FDR wherever inputs are truly null, while uncalibrated derivative rankings breach the target by up to 2x and a Bernstein-von Mises cutoff by 2.2x; at matched FDR it loses no power; it holds under a Matérn kernel and input correlation up to 0.99; on real data with planted and authentic null inputs it admits 5-12x fewer spurious inputs; it costs 5-18% of the GP fit; and a block-averaged variant retains validity at cost linear in $n$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33549",
  "author_total": 1,
  "authors": [
    {
      "name": "Jia Cai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2m3swvpw7xs4b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33549",
  "fulltext_url": null,
  "id": "2m3swvpw7xs4b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33549",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Gaussian Processes and Bayesian Inference"
    ]
  ],
  "openalex": "W7214791196",
  "pdf_url": "https://arxiv.org/pdf/2609.33549",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2m3swvpw7xs4b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.33549",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33549"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Calibrated Derivative-Process Sensitivity for Gaussian-Process Variable Selection",
  "title_text": "Calibrated Derivative-Process Sensitivity for Gaussian-Process Variable Selection",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:26Z",
  "url": "https://research.draconitic.com/paper/2m3swvpw7xs4b",
  "venue": "arXiv",
  "versions": []
}