{
  "abstract": "Personalized federated learning can improve estimation for high-dimensional time series while preserving client-specific dynamics. However, parameter heterogeneity creates a fundamental ambiguity between shared and personalized structure. We introduce the principle of personalization diversity, under which genuinely personalized effects recur in only a limited fraction of clients. Based on this principle, we propose PerFeCT-VAR, Personalized Federated Vector Autoregression via Frequency-Capped Thresholding, which decomposes each client-specific transition matrix into shared low-rank dynamics, shared sparse links, and personalized sparse departures. A cross-client frequency cap yields a sharp shared--personalized separation threshold and motivates frequency-capped thresholding for federated estimation. Our theory further accounts for heterogeneous client distributions through a distributional compatibility condition and establishes joint linear convergence of the shared and personalized components. Under sufficient personalization diversity, the shared dynamics retain federated total-sample-size gains while the personalized components achieve client-level accuracy. Simulations and an application to multi-store retail revenue data demonstrate the predictive and interpretive benefits of the proposed framework.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04474",
  "author_total": 4,
  "authors": [
    {
      "name": "Zhiyun Fan"
    },
    {
      "name": "Xiaoyu Zhang"
    },
    {
      "name": "Guodong Li"
    },
    {
      "name": "Di Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/03pvbc86d26xt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04474",
  "fulltext_url": null,
  "id": "03pvbc86d26xt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04474",
  "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",
      "stat.ME"
    ],
    [
      "openalex",
      "1702|Privacy-Preserving Technologies in Data"
    ]
  ],
  "openalex": "W7220744175",
  "pdf_url": "https://arxiv.org/pdf/2610.04474",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/03pvbc86d26xt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:16Z",
      "native_id": "2610.04474",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04474"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Personalized Federated Vector Autoregression with Personalization Diversity",
  "title_text": "Personalized Federated Vector Autoregression with Personalization Diversity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:16Z",
  "url": "https://research.draconitic.com/paper/03pvbc86d26xt",
  "venue": "arXiv",
  "versions": []
}