{
  "abstract": "We introduce a Stein variational framework for sampling from a target density $p\\propto e^{-U}$ when the target potential $U$ is possibly non-smooth. The key idea is to introduce a smoother reference potential $U_0$ and the anchor weight $a=e^{U-U_0}$. The resulting anchored Stein variational gradient descent (SVGD) algorithm is able to target $p\\propto e^{-U}$ without computing the gradient of $U$ and include standard SVGD as a special case. In particular, we allow the target potential $U$ to be locally Lipschitz while the reference potential $U_0$ is continuously differentiable, along with other suitable assumptions. Under this low regularity regime, we establish a Kullback-Leibler first variation formula for anchored perturbations, identify the corresponding steepest descent direction in the reproducing kernel Hilbert space and prove a nonasymptotic convergence bound for the anchored SVGD algorithm in terms of an anchored kernelized Stein discrepancy. Finally, we also provide guidance on constructing a suitable reference potential $U_0$ based on $U$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36018",
  "author_total": 3,
  "authors": [
    {
      "name": "Thanh Dang"
    },
    {
      "name": "Matthew X. Burns"
    },
    {
      "name": "Jiaming Liang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5q5cvyd2kjk36.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36018",
  "fulltext_url": null,
  "id": "5q5cvyd2kjk36",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36018",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7224095600",
  "pdf_url": "https://arxiv.org/pdf/2610.36018",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5q5cvyd2kjk36.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:59Z",
      "native_id": "2610.36018",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36018"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Anchored Stein Variational Gradient Descent Algorithm for Non-smooth Sampling",
  "title_text": "Anchored Stein Variational Gradient Descent Algorithm for Non-smooth Sampling",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:59Z",
  "url": "https://research.draconitic.com/paper/5q5cvyd2kjk36",
  "venue": "arXiv",
  "versions": []
}