{
  "abstract": "A classical approach for importance sampling (IS) of a rare event is to tilt the measure using its large deviation minimizer, thereby shifting the proposal mean towards the event set. While this tilt is log-efficient, we show that the coefficient of variation of the resulting estimator still grows like $\\varepsilon^{-1/4}$ in the small-noise limit $\\varepsilon\\downarrow0$. Motivated by sharp large deviation asymptotics and the local geometry of the event set at the minimizer, we propose improvements using a control variate or an anisotropic, non-Gaussian proposal. We prove, up to truncations that hold with high probability, and confirm empirically in high-dimensional examples, that the former bounds the coefficient of variation and the latter makes it vanish, so that a bounded number of samples suffices. Our analysis addresses both the coefficient of variation of the different proposals and their necessary and sufficient sample size based on the Kullback--Leibler divergence of the IS target from the proposal; both yield the same rates in $\\varepsilon$. We demonstrate the resulting samplers, including a variant that blends the classical and the new proposal across noise levels, for a stochastic Korteweg--de Vries equation with thousands of random inputs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27434",
  "author_total": 4,
  "authors": [
    {
      "name": "Mingxin Li"
    },
    {
      "name": "Hans Reimann"
    },
    {
      "name": "Timo Schorlepp"
    },
    {
      "name": "Georg Stadler"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9ce39p8521m9m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27434",
  "fulltext_url": null,
  "id": "9ce39p8521m9m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27434",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
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      "math.PR"
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      "2613|Markov Chains and Monte Carlo Methods"
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  "openalex": "W7223085721",
  "pdf_url": "https://arxiv.org/pdf/2610.27434",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9ce39p8521m9m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27434",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27434"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Beyond exponential tilting: sharp asymptotics and improved importance sampling for rare events",
  "title_text": "Beyond exponential tilting: sharp asymptotics and improved importance sampling for rare events",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:13Z",
  "url": "https://research.draconitic.com/paper/9ce39p8521m9m",
  "venue": "arXiv",
  "versions": []
}