{
  "abstract": "Self-distillation has emerged as a promising technique for improving model performance in modern machine learning systems. We develop the statistical foundations of self-distillation in high-dimensional linear regression by introducing and analyzing a broad class of estimators, namely spectral shrinkage estimators. We consider both spiked and general covariance matrices. For the former, we establish that when the covariance has $s$ distinct spikes, $s$-step self-distillation achieves optimal prediction among spectral shrinkage estimators, outperforming well-known estimators in statistics and machine learning. Moreover, we show that $s$ steps are necessary for optimality: any $(s-k)$-step distilled estimator is strictly suboptimal for $1 \\leq k \\leq s$. For general covariance matrices, we show that self-distillation approaches the optimal limiting prediction risk among continuous spectral shrinkage estimators as the number of distillation steps increases. We further develop a generalized cross-validation procedure for selecting the distillation parameters from data and establish an asymptotic oracle guarantee for the resulting estimator. We also study a federated approach where multiple data centers share spectral shrinkage estimators and a common server seeks to aggregate them to achieve optimal performance. In this case, we find that the best local rule again takes the form of self-distillation, though it differs from the optimal rule when data are hosted centrally on a single server. Together, our results explain why self-distillation improves predictive performance and provide a broader statistical framework that connects it to classical shrinkage-based methods.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.17778",
  "author_total": 3,
  "authors": [
    {
      "name": "Radu Lecoiu"
    },
    {
      "name": "Debarghya Mukherjee"
    },
    {
      "name": "Pragya Sur"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/995pszzrfrn27.bib",
  "cited_by": 4,
  "doi": "10.48550/arxiv.2605.17778",
  "fulltext_url": null,
  "id": "995pszzrfrn27",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.17778",
  "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",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Statistical Methods and Inference"
    ]
  ],
  "openalex": "W7161711759",
  "pdf_url": "https://arxiv.org/pdf/2605.17778",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/995pszzrfrn27.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T06:21:07Z",
      "native_id": "2605.17778",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.17778"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Self-Distillation is Optimal Among Spectral Shrinkage Estimators",
  "title_text": "Self-Distillation is Optimal Among Spectral Shrinkage Estimators",
  "type": "preprint",
  "updated_at": "2026-11-10T06:21:13Z",
  "url": "https://research.draconitic.com/paper/995pszzrfrn27",
  "venue": "arXiv",
  "versions": []
}