{
  "annotation_id": "50edbeea-366c-4c38-a169-441d7a64fba5",
  "date_created": "2026-02-17T05:53:15.772000Z",
  "date_modified": "2026-02-17T05:53:15.772000Z",
  "file_hash": "55d964d13fad112380ef5899c063e89f156a62d9c118db5695b0f4977a88b109",
  "private": false,
  "record": {
    "abstract": "Finite-time central limit theorem (CLT) rates play a central role in modern machine learning. In this paper, we study CLT rates for multivariate dependent data in Wasserstein-$p$ ($W_p$) distance, for general $p \\geq 1$. We focus on two fundamental dependence structures that commonly arise in machine learning: locally dependent sequences and geometrically ergodic Markov chains. In both settings, we establish the first optimal $O(n^{-1/2})$ rate in $W_1$, as well as the first $W_p$ ($p\\ge 2$) CLT rates under mild moment assumptions, substantially improving the best previously known bounds in these dependent-data regimes. As an application of our optimal $W_1$ rate for locally dependent sequences, we further obtain the first optimal $W_1$-CLT rate for multivariate $U$-statistics.\n  On the technical side, we derive a tractable auxiliary bound for $W_1$ Gaussian approximation errors that is well suited for studying dependent data. For Markov chains, we further prove that the regeneration time of the split chain associated with a geometrically ergodic chain has a geometric tail without assuming strong aperiodicity or other restrictive conditions. These tools may be of independent interests and enable our optimal $W_1$ rates and underpin our $W_p$ ($p\\ge 2$) results.",
    "arxiv_id": "2601.08184",
    "authors": [
      "Yixuan Zhang",
      "Qiaomin Xie"
    ],
    "categories": [
      "math.PR",
      "cs.LG",
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Wasserstein-p Central Limit Theorem Rates: From Local Dependence to Markov Chains",
    "url": "https://arxiv.org/abs/2601.08184",
    "version": "v2"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "bbbf4c66-9a9e-4901-ae8b-02ec4bbe72e7",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}