{
  "abstract": "The BROJA partial information decomposition provides an operationally motivated way to separate the information that two sources carry about a target into unique, redundant, and synergistic components. For continuous and high-dimensional variables, however, computing the BROJA decomposition requires solving a difficult optimization problem. Previous work showed that, when each source-target pair is jointly Gaussian, the problem can be reduced to finite-dimensional numerical optimization. Here, we derive a closed-form solution to this optimization problem, enabling direct computation of the BROJA decomposition in the general multivariate Gaussian setting. The resulting closed-form expression enables speedups exceeding two orders of magnitude for high-dimensional Gaussian BROJA PID. Code is available at https://github.com/brainsandmachines/Eigen_PID.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13464",
  "author_total": 3,
  "authors": [
    {
      "name": "Ohad Sheelo"
    },
    {
      "name": "Tal Golan"
    },
    {
      "name": "Ari Pakman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dxx6sf9ae9jfa.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13464",
  "fulltext_url": null,
  "id": "dxx6sf9ae9jfa",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13464",
  "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",
      "stat.ML"
    ],
    [
      "openalex",
      "2805|Functional Brain Connectivity Studies"
    ]
  ],
  "openalex": "W7221505291",
  "pdf_url": "https://arxiv.org/pdf/2610.13464",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dxx6sf9ae9jfa.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.13464",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13464"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Gaussian BROJA Partial Information Decomposition in Closed Form",
  "title_text": "Gaussian BROJA Partial Information Decomposition in Closed Form",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:46Z",
  "url": "https://research.draconitic.com/paper/dxx6sf9ae9jfa",
  "venue": "arXiv",
  "versions": []
}