{
  "abstract": "Stability Selection resamples the observations but leaves the design untouched, so it cannot reject an irrelevant feature that is correlated with the relevant ones in a way that violates the irrepresentable condition. Such a feature (a ``confounder'') is selected in a substantial fraction of resamples, and the exchangeability behind the false-positive bound of Stability Selection fails. We propose 2D Stability Selection (2D-SS), which aggregates selection frequencies over half-samples and over a grid of injected design noise, and reduces to Stability Selection at zero noise. Because input noise acts, in expectation, as Tikhonov regularisation, a jittered Lasso fit is a noisy elastic net whose support recovery is governed by a noise-indexed irrepresentable condition. Jittering can therefore repair designs in which confounders violate the Lasso condition, although it can also hurt. We give the noise level at which a violated feature's statistic vanishes (for uncorrelated relevant features), exact-recovery guarantees for a single fit, conditions under which aggregation over noise levels recovers the support, and a complementary-pairs bound on the expected number of false positives, carried over from Stability Selection to the noise-aggregated procedure, for a fixed threshold or a size-matched selector. The procedure takes no measurement-error covariance as input, although the guarantees assume i.i.d.\\ Gaussian measurement error. In simulations 2D-SS excludes confounders that Stability Selection includes, and its size-matched version stays below the nominal closed-form false-positive bound in all 240 simulated cells, whereas Stability Selection exceeds it in 21; it does not generally improve on Stability Selection in $F_1$ and is lower at low noise. It is useful when stable but wrong selections are the concern.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.02205",
  "author_total": 3,
  "authors": [
    {
      "name": "Mahdi Nouraie"
    },
    {
      "name": "Houying Zhu"
    },
    {
      "name": "Samuel Muller"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/777g6750tyfb4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.02205",
  "fulltext_url": null,
  "id": "777g6750tyfb4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.02205",
  "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"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "2613|Statistical Methods and Inference"
    ]
  ],
  "openalex": "W7160272441",
  "pdf_url": "https://arxiv.org/pdf/2605.02205",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/777g6750tyfb4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:43Z",
      "native_id": "2605.02205",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.02205"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "2D Stability Selection: Design Jittering to Exclude Correlated Irrelevant Features",
  "title_text": "2D Stability Selection: Design Jittering to Exclude Correlated Irrelevant Features",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:38Z",
  "url": "https://research.draconitic.com/paper/777g6750tyfb4",
  "venue": "arXiv",
  "versions": []
}