{
  "id": "2505.16713",
  "version": "v2",
  "published": "2025-05-22T14:14:50.000Z",
  "updated": "2025-06-26T06:57:11.000Z",
  "title": "Sharp concentration of uniform generalization errors in binary linear classification",
  "authors": [
    "Shogo Nakakita"
  ],
  "comment": "26 pages, 1 figure; minor edits to improve readability",
  "categories": [
    "stat.ML",
    "cs.LG",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "We examine the concentration of uniform generalization errors around their expectation in binary linear classification problems via an isoperimetric argument. In particular, we establish Poincar\\'{e} and log-Sobolev inequalities for the joint distribution of the output labels and the label-weighted input vectors, which we apply to derive concentration bounds. The derived concentration bounds are sharp up to moderate multiplicative constants by those under well-balanced labels. In asymptotic analysis, we also show that almost sure convergence of uniform generalization errors to their expectation occurs in very broad settings, such as proportionally high-dimensional regimes. Using this convergence, we establish uniform laws of large numbers under dimension-free conditions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2025-06-26T06:57:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "uniform generalization errors",
      "sharp concentration",
      "binary linear classification problems",
      "concentration bounds",
      "isoperimetric argument"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}