{
  "abstract": "We study deterministic relative approximation of the total variation distance between high-dimensional distributions given by succinct descriptions. We develop an abstract deterministic approximation framework based on representing the total variation distance as a support function of a low-dimensional zonotope. As applications, we obtain FPTASs for several models. Given two mixtures of product distributions over $[q]^n$ with a total of $K$ component distributions, our algorithm approximates their TV-distance within a factor of $1+\\varepsilon$ in time $\\widetilde O_K(nq(n/\\varepsilon)^{2K})$. We also give an FPTAS for mixtures of $n$-step Markov chains over $[q]^n$ with a total of $K$ component distributions, with running time $\\widetilde O_K(nq^2(n/\\varepsilon)^{2K})$. Finally, for two latent-tree Ising models with the same underlying tree topology, we give an FPTAS for the TV-distance between their leaf marginals in time $O(|V|^{13}\\varepsilon^{-12})$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24235",
  "author_total": 1,
  "authors": [
    {
      "name": "Yucheng Fu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6exdx1arnk577.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24235",
  "fulltext_url": null,
  "id": "6exdx1arnk577",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24235",
  "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.DS"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "1703|Complexity and Algorithms in Graphs"
    ]
  ],
  "openalex": "W7214010020",
  "pdf_url": "https://arxiv.org/pdf/2609.24235",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6exdx1arnk577.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24235",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24235"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "On Deterministically Computing Total Variation Distance via Zonotope Compression",
  "title_text": "On Deterministically Computing Total Variation Distance via Zonotope Compression",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/6exdx1arnk577",
  "venue": "arXiv",
  "versions": []
}