{
  "abstract": "Density ratios quantify distribution shift from a probability-mass point of view, whereas displacement fields describe, from a dynamical point of view, how one distribution is transported onto another. Although both offer complementary insights, they are usually estimated separately, and converting one into the other requires post-processing. In this paper, we estimate the density ratio between a target and a base distribution by parametrizing it through a displacement field acting on the base: the log-ratio is modeled as minus the Stein operator of the base applied to the field, up to a normalizing constant. This gives both statistical and dynamical descriptions of the distribution shift through a single convex optimization problem. Iterating this estimate-and-move step gives two inference algorithms: push-forward moves the model and corrects a pretrained sampler without retraining it, whereas pull-back moves the data closer to the base and fits a transformation model one layer at a time. Applications to distribution shift in simulation-based inference and to nonlinear independent component analysis illustrate the benefits and limitations of the approach.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12437",
  "author_total": 1,
  "authors": [
    {
      "name": "Song Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/82mqx3e27rsbm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12437",
  "fulltext_url": null,
  "id": "82mqx3e27rsbm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12437",
  "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": "W7221188337",
  "pdf_url": "https://arxiv.org/pdf/2610.12437",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/82mqx3e27rsbm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:26Z",
      "native_id": "2610.12437",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12437"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Density Ratio Estimation with Stein Displacement Fields",
  "title_text": "Density Ratio Estimation with Stein Displacement Fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:26Z",
  "url": "https://research.draconitic.com/paper/82mqx3e27rsbm",
  "venue": "arXiv",
  "versions": []
}