{
  "abstract": "A normal--inverse-gamma (NIG) latent hierarchy has four parameters, but its induced latent law does not identify all four. For $σ^2\\sim\\mathrm{InvGamma}(α,β)$, $μ\\midσ^2\\sim\\mathcal{N}(γ,σ^2/ν)$, and $z\\midμ,σ^2\\sim\\mathcal{N}(μ,σ^2)$, the marginal law of $z$ depends on $(ν,β)$ only through $c=β(1+1/ν)$. Hence the reconstruction-visible parameter space is the three-dimensional quotient $(γ,α,c)$, with a one-dimensional fiber degree of freedom. For a fixed hierarchical variational objective, exact partial minimization of the forward KL divergence to a complete NIG prior selects a unique prior-relative representative on each fiber, yielding an exact three-coordinate reduction with the same optimum as the four-coordinate objective. Writing $ρ_0=2β_0/ν_0$ and $T=c/\\{α[(γ-γ_0)^2+ρ_0]\\}$, we show that inverse canonical allocation $1/ν_{\\rm can}$ is an explicit strictly increasing function of $T$. For $α>1$, the ratio $u_{\\rm epi}/u_{\\rm var}=1/ν_{\\rm can}$ is therefore determined by the quotient state and prior; for rank-only use under a common calibration, $T$ contains the same coordinatewise ordinal information. The residual prior gauge is characterized rather than eliminated: $(γ_0,ρ_0)$ govern ordinal dependence, while $(ν_0,α_0)$ determine numerical calibration and the analytic ceiling of $1/ν_{\\rm can}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27853",
  "author_total": 1,
  "authors": [
    {
      "name": "Ge Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/30jg86rxv177n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27853",
  "fulltext_url": null,
  "id": "30jg86rxv177n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27853",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "cs.NE"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1702|Gaussian Processes and Bayesian Inference"
    ]
  ],
  "openalex": "W7214234772",
  "pdf_url": "https://arxiv.org/pdf/2609.27853",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/30jg86rxv177n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27853",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27853"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Theoretical Study on the Evidential Learning-based Variational Autoencoder",
  "title_text": "Theoretical Study on the Evidential Learning-based Variational Autoencoder",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:06Z",
  "url": "https://research.draconitic.com/paper/30jg86rxv177n",
  "venue": "arXiv",
  "versions": []
}