{
  "id": "2505.06531",
  "version": "v1",
  "published": "2025-05-10T06:26:12.000Z",
  "updated": "2025-05-10T06:26:12.000Z",
  "title": "High-Dimensional Importance-Weighted Information Criteria: Theory and Optimality",
  "authors": [
    "Yong-Syun Cao",
    "Shinpei Imori",
    "Ching-Kang Ing"
  ],
  "categories": [
    "stat.ML",
    "cs.LG",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "Imori and Ing (2025) proposed the importance-weighted orthogonal greedy algorithm (IWOGA) for model selection in high-dimensional misspecified regression models under covariate shift. To determine the number of IWOGA iterations, they introduced the high-dimensional importance-weighted information criterion (HDIWIC). They argued that the combined use of IWOGA and HDIWIC, IWOGA + HDIWIC, achieves an optimal trade-off between variance and squared bias, leading to optimal convergence rates in terms of conditional mean squared prediction error. In this article, we provide a theoretical justification for this claim by establishing the optimality of IWOGA + HDIWIC under a set of reasonable assumptions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-10T06:26:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "high-dimensional importance-weighted information criterion",
      "optimality",
      "conditional mean squared prediction error",
      "importance-weighted orthogonal greedy algorithm",
      "high-dimensional misspecified regression models"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}