Theoretical Study on the Evidential Learning-based Variational Autoencoder
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 ...
| Authors | Ge Wang |
|---|---|
| Primary category | stat.ML |
| Published | 19 August 2026 |
| Last updated at source | 19 August 2026 |
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