{
  "abstract": "Barycenter models, based on stochastic and deterministic optimal transport bridges between probability measures, have proven to be useful for supervised and unsupervised learning for (probability) measure-valued data. In this paper, we utilize the directional asymmetry and dual drift-diffusion control arising in the recently proposed Schrödinger-Bass Bridge (SBB) between two measures, and propose \\textit{SBB-encoder}, \\textit{SBB-decoder}, \\textit{SBB-symmetric}, and \\textit{SBB-Markovian} barycenter models. For each of these novel models, our first theoretical result establishes the existence of the SBB-barycenter under mild assumptions. Our second theoretical result characterizes the decoder SBB-barycenter of Gaussians where we show that for Gaussian input measures, the decoder formulation admits a Gaussian minimizer, reducing barycenter computation to a finite-dimensional optimization and yielding a compact algorithm. For general input measures, we derive a hybrid Wasserstein gradient particle descent scheme for all four formulations using the SBB dual representation. Finally, we utilize these algorithms for solving distributional-inverse/interpolation problems arising in the context of spatial images and single-cell RNA sequencing data, where we show that the SBB-decoder and Markovian barycenter allow us to interpolate between successive time points. Results show that our method outperforms existing barycenter models for measure interpolation and inference.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29227",
  "author_total": 4,
  "authors": [
    {
      "name": "Ngoc-Hai Nguyen"
    },
    {
      "name": "Thuan Nguyen"
    },
    {
      "name": "Prakash Ishwar"
    },
    {
      "name": "Shuchin Aeron"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dhz5a4f6qw32e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29227",
  "fulltext_url": null,
  "id": "dhz5a4f6qw32e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29227",
  "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",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7223248427",
  "pdf_url": "https://arxiv.org/pdf/2610.29227",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dhz5a4f6qw32e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:29Z",
      "native_id": "2610.29227",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29227"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Schrödinger-Bass Bridge Barycenter Models for Measure-Valued Data",
  "title_text": "Schrödinger-Bass Bridge Barycenter Models for Measure-Valued Data",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:29Z",
  "url": "https://research.draconitic.com/paper/dhz5a4f6qw32e",
  "venue": "arXiv",
  "versions": []
}