{
  "abstract": "The manifold hypothesis posits that high-dimensional data are concentrated near a low-dimensional embedded manifold. Recent advances in mixture variational autoencoders (VAEs) provide a powerful tool for extracting such underlying structure in a faithful manner. The resulting geometric structure naturally introduces local and global relationships among variables, thereby providing a systematic way of imputing missing data. We propose a model-based imputation method that enables sampling from \\( p(\\bm{x}_{\\mathrm{mis}} \\mid \\bm{x}_{\\mathrm{obs}}) \\) via a sampling-importance-resampling (SIR) procedure, which can be further augmented with a joint diffusion model in the latent space. Our method imputes missing data while respecting the underlying geometry, achieves competitive performance compared to state-of-the-art procedures, quantifies uncertainty in the imputations, and is model-based, thereby enabling on-the-fly imputation without rerunning the entire procedure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.03641",
  "author_total": 3,
  "authors": [
    {
      "name": "Zelong Bi"
    },
    {
      "name": "Amuchechukwu Ibenegbu"
    },
    {
      "name": "Sarat Moka"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3rbpfpvyp2crz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.03641",
  "fulltext_url": null,
  "id": "3rbpfpvyp2crz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.03641",
  "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|Statistical Methods and Bayesian Inference"
    ]
  ],
  "openalex": "W7167608371",
  "pdf_url": "https://arxiv.org/pdf/2607.03641",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3rbpfpvyp2crz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:51Z",
      "native_id": "2607.03641",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.03641"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Missing Data Imputation under Manifold Hypothesis",
  "title_text": "Missing Data Imputation under Manifold Hypothesis",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:51Z",
  "url": "https://research.draconitic.com/paper/3rbpfpvyp2crz",
  "venue": "arXiv",
  "versions": []
}