{
  "id": "2406.03171",
  "version": "v1",
  "published": "2024-06-05T12:03:27.000Z",
  "updated": "2024-06-05T12:03:27.000Z",
  "title": "High-Dimensional Kernel Methods under Covariate Shift: Data-Dependent Implicit Regularization",
  "authors": [
    "Yihang Chen",
    "Fanghui Liu",
    "Taiji Suzuki",
    "Volkan Cevher"
  ],
  "comment": "ICML 2024",
  "categories": [
    "stat.ML",
    "cs.LG"
  ],
  "abstract": "This paper studies kernel ridge regression in high dimensions under covariate shifts and analyzes the role of importance re-weighting. We first derive the asymptotic expansion of high dimensional kernels under covariate shifts. By a bias-variance decomposition, we theoretically demonstrate that the re-weighting strategy allows for decreasing the variance. For bias, we analyze the regularization of the arbitrary or well-chosen scale, showing that the bias can behave very differently under different regularization scales. In our analysis, the bias and variance can be characterized by the spectral decay of a data-dependent regularized kernel: the original kernel matrix associated with an additional re-weighting matrix, and thus the re-weighting strategy can be regarded as a data-dependent regularization for better understanding. Besides, our analysis provides asymptotic expansion of kernel functions/vectors under covariate shift, which has its own interest.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-05T12:03:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "covariate shift",
      "high-dimensional kernel methods",
      "data-dependent implicit regularization",
      "paper studies kernel ridge regression",
      "asymptotic expansion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}