{
  "abstract": "Bayesian inference for latent point process intensities often relies on per-dataset sampling or optimization, making repeated inference computationally expensive. We propose a neural-network-based amortized variational framework that learns a reusable inference rule mapping a variable number of replicated point patterns to a distribution over their shared latent intensity. Trained from event times using the point process likelihood, the model learns an amortized inference rule without ground-truth intensity supervision. At test time, it performs inference of the latent distribution in a forward pass. On synthetic data, additional realizations improve intensity recovery and yield narrower credible intervals with broadly stable coverage. Our method is tested on bicycle-sharing data and achieves the highest mean held-out log likelihood among the evaluated methods while requiring substantially less inference time than the Log-Gaussian Cox Process baseline.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16669",
  "author_total": 3,
  "authors": [
    {
      "name": "Wenqing Liu"
    },
    {
      "name": "Xenia Miscouridou"
    },
    {
      "name": "Déborah Sulem"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4qx7jbj94f26c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16669",
  "fulltext_url": null,
  "id": "4qx7jbj94f26c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16669",
  "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.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W7221829342",
  "pdf_url": "https://arxiv.org/pdf/2610.16669",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4qx7jbj94f26c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:26Z",
      "native_id": "2610.16669",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16669"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Amortized Variational Inference of Latent Intensities from Replicated Point Patterns",
  "title_text": "Amortized Variational Inference of Latent Intensities from Replicated Point Patterns",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:26Z",
  "url": "https://research.draconitic.com/paper/4qx7jbj94f26c",
  "venue": "arXiv",
  "versions": []
}