{
  "abstract": "We study high-dimensional nonparametric regression under multisource covariate shift, where $\\mathrm J$ sources of training data share a common regression function but differ in their covariate distributions, sample sizes, and noise variances. Our goal is to combine these sources to estimate the regression function accurately under a target covariate distribution. We propose an oracle weighted neural estimator and establish its minimax optimality up to logarithmic factors through matching upper and lower bounds. The resulting rate is $\\mathsf n_{\\rm eff}^{-2p/(2p+K)}$, where $p$ and $K$ denote the effective smoothness and dimension of the regression function, and the effective sample size is \\begin{align} \\mathsf n_{\\rm eff} =\\sum_{j=1}^{\\mathrm J} \\frac{n_j}{(1+σ_{ρ,j})σ_{ε,j}^{2}}. \\nonumber \\end{align} Here, $n_j$ is the sample size of source $j$, $σ_{ε,j}^{2}$ is its noise variance, and $σ_{ρ,j}$ controls the deviation between the covariate distribution of source $j$ and the target covariate distribution. We also develop an adaptive procedure that requires no knowledge of source noise variances or covariate-shift parameters. Under suitable conditions, this procedure attains the oracle minimax rate up to logarithmic factors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40331",
  "author_total": 4,
  "authors": [
    {
      "name": "Chenghao Xu"
    },
    {
      "name": "Haotian Xu"
    },
    {
      "name": "Shivam Kumar"
    },
    {
      "name": "Daren Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dyz2vehtx2632.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40331",
  "fulltext_url": null,
  "id": "dyz2vehtx2632",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40331",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "arxiv",
      "stat.TH"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40331",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dyz2vehtx2632.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.40331",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40331"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Optimal Neural Estimation for High-Dimensional Nonparametric Regression under Multisource Covariate Shift",
  "title_text": "Optimal Neural Estimation for High-Dimensional Nonparametric Regression under Multisource Covariate Shift",
  "type": "preprint",
  "updated_at": "2026-11-01T12:21:00Z",
  "url": "https://research.draconitic.com/paper/dyz2vehtx2632",
  "venue": "arXiv",
  "versions": []
}