{
  "id": "2401.12272",
  "version": "v1",
  "published": "2024-01-22T16:24:04.000Z",
  "updated": "2024-01-22T16:24:04.000Z",
  "title": "Transfer Learning for Nonparametric Regression: Non-asymptotic Minimax Analysis and Adaptive Procedure",
  "authors": [
    "T. Tony Cai",
    "Hongming Pu"
  ],
  "categories": [
    "stat.ML",
    "cs.LG"
  ],
  "abstract": "Transfer learning for nonparametric regression is considered. We first study the non-asymptotic minimax risk for this problem and develop a novel estimator called the confidence thresholding estimator, which is shown to achieve the minimax optimal risk up to a logarithmic factor. Our results demonstrate two unique phenomena in transfer learning: auto-smoothing and super-acceleration, which differentiate it from nonparametric regression in a traditional setting. We then propose a data-driven algorithm that adaptively achieves the minimax risk up to a logarithmic factor across a wide range of parameter spaces. Simulation studies are conducted to evaluate the numerical performance of the adaptive transfer learning algorithm, and a real-world example is provided to demonstrate the benefits of the proposed method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-22T16:24:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "transfer learning",
      "nonparametric regression",
      "non-asymptotic minimax analysis",
      "adaptive procedure",
      "logarithmic factor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}