{
  "abstract": "Consider an \"unsupervised classification\" setting, where the goal is to learn a predictor of the categorical class variable $X$ using the categorical feature variables $Y_1,\\ldots,Y_m$, but we can only train the predictor on $m+1$ totally unpaired datasets, where each dataset only consists of unordered samples of one of the variables $X,Y_{1},\\ldots,Y_{m}$. Although this problem is highly underdetermined, we demonstrate that, under the assumption that a predictor with small cross entropy loss exists, we can find a good predictor by coupling the marginal distributions of $X,Y_1,\\ldots,Y_m$ in a manner that minimizes the conditional entropy $H(X|Y_1,\\ldots,Y_m)$. This problem, which we call minimum conditional entropy coupling (MCEC), is a generalization of the widely studied minimum entropy coupling problem (where $m=1$). Although the MCEC problem is NP-hard, we give an algorithm with a time complexity that is polynomial in $N$, which gives a coupling with conditional entropy within $O(\\log \\log N)$ from the optimum, where $N$ is the dimension of the output coupling. We also evaluate the performance of the MCEC predictor on synthetic and real-world datasets.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.16229",
  "author_total": 3,
  "authors": [
    {
      "name": "Cheuk Ting Li"
    },
    {
      "name": "Jun Chen"
    },
    {
      "name": "Shahab Asoodeh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fspmjvn0sbqb6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.16229",
  "fulltext_url": null,
  "id": "fspmjvn0sbqb6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.16229",
  "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.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Probability and Statistical Research"
    ]
  ],
  "openalex": "W7161546886",
  "pdf_url": "https://arxiv.org/pdf/2605.16229",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fspmjvn0sbqb6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2605.16229",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.16229"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Learning from Totally Unpaired Data via Minimum Conditional Entropy Coupling",
  "title_text": "Learning from Totally Unpaired Data via Minimum Conditional Entropy Coupling",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:26Z",
  "url": "https://research.draconitic.com/paper/fspmjvn0sbqb6",
  "venue": "arXiv",
  "versions": []
}