{
  "abstract": "Robust linear fits can resist response contamination yet remain too dense or unstable for useful global explanations. We propose penalized distillation, which fits a smoothly clipped absolute deviation (SCAD) estimator to a robust initial estimator's empirical fitted surface along a safeguarded coordinate-descent path and evaluates candidate states separately for fidelity, parsimony, perturbation stability, and held-out prediction. The new results attach to the states the algorithm actually computes. Conditional on a fixed uncontaminated design, deterministic bounds transfer response-replacement boundedness from the initial fit to every retained path state. Turning to fixed dimension, we characterize the oracle-support branch by its empirical-Gram projection and influence function, give conditions for covariance-weighted least-squares approximation equivalence, and establish a path-conditional generalized information criterion. By contrast, at large dimension-to-sample ratios the full-coordinate robust fit collapses without warning, and screening restores the construction. Under a sure-screening framework, the robustness bound and the support and selection guarantees transfer to the screened fit. Simulations separate robustness transfer from support recovery, efficiency, and computation across the dimension-to-sample ratio, with p up to 240, and the signal density, which isolates what the sparse stage adds once the screen over-selects. In a duplicate-grouped superconductivity study, the distilled estimator remains predictively stable under prespecified training-response shifts but retains 66.8--68.8 of 81 slopes. Stronger sparsification reduces the model to 12.6--14.0 slopes only at visible fidelity and prediction cost. Distillation therefore preserves predictive stability on these data without substantiating a compact coordinate-level explanation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23937",
  "author_total": 2,
  "authors": [
    {
      "name": "Wooyoung Shin"
    },
    {
      "name": "Seunghwan Park"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7vgp90ceb01h1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23937",
  "fulltext_url": null,
  "id": "7vgp90ceb01h1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23937",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "2613|Statistical Methods and Inference"
    ]
  ],
  "openalex": "W7214041421",
  "pdf_url": "https://arxiv.org/pdf/2609.23937",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7vgp90ceb01h1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:33Z",
      "native_id": "2609.23937",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23937"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Sparse Regression Distilled from a Single Robust Fit",
  "title_text": "Sparse Regression Distilled from a Single Robust Fit",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:33Z",
  "url": "https://research.draconitic.com/paper/7vgp90ceb01h1",
  "venue": "arXiv",
  "versions": []
}