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Copula Active Subspaces I: A Score-Covariance Method for Reduced-Order Non-Gaussian Density Estimation — arXiv:2609.36142

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.36142
License (as archived): CC0-1.0
Archived: 2026-10-07T18:00:11.969Z
SHA-256 of the archived text: 228232aaef4e6a7a9a6d5737df97795d5cfbcc4d55e7731851599b7a4070a1a5
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How to cite

Copula Active Subspaces I: A Score-Covariance Method for Reduced-Order Non-Gaussian Density Estimation — arXiv:2609.36142 — arXiv (en), https://arxiv.org/abs/2609.36142 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_44206fa28eea (Metraipolis archive dc_44206fa28eea, sha256 228232aaef4e6a7a9a6d5737df97795d5cfbcc4d55e7731851599b7a4070a1a5)

BibTeX

@misc{dc44206fa28eea,
  title = {Copula Active Subspaces I: A Score-Covariance Method for Reduced-Order Non-Gaussian Density Estimation — arXiv:2609.36142},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.36142},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_44206fa28eea; sha256 228232aaef4e6a7a9a6d5737df97795d5cfbcc4d55e7731851599b7a4070a1a5},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.36142. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In Bayesian inference problems with non-Gaussian observation noise, the posterior is only as accurate as the noise density, and gradient-based samplers need that density and its gradient evaluable pointwise, whether from an explicit expression or from code, and without an inner solve. We propose Copula Active Subspaces (CAS) to represent this noise density. A componentwise rank transform isolates the noise law's dependence in its copula, and a rank-$r$ reduction keeps only the directions along which that dependence varies. These directions are the leading eigenvectors of the copula score covariance $\boldsymbol{C} := \mathrm{Cov}_{\pi_{\boldsymbol{Z}}}(\nabla\log c^{Z})$, which is what makes the reduction a copula active subspace. Because $\boldsymbol{C}$ vanishes when the coordinates are independent, these are directions of dependence, which the covariance of the data need not identify. From this construction follow a Gaussian-reference KL divergence bound with the explicit constant $\tfrac{1}{2}$, minimized over all rank-$r$ reductions by exactly this eigenspace; a diagnostic for the error the reduction leaves behind, computable from the samples alone; and, from Hermite score matching, a reduced log-density and gradient in closed form, with the truncation orders and the Stage-2 regularization constants chosen on validation samples. The reduction replaces a $d$-dimensional density estimation problem by an $r$-dimensional one. On a $d=20$ noise law and a Bayesian inference problem with that noise, CAS lowers noise KL divergence more than fivefold and posterior KL divergence more than sevenfold against Gaussian-copula, product-of-marginals, and PCA-subspace baselines, and lowers noise KL divergence by factors of about $3.5$ and $2.7$ on two further $d=20$ examples.

Tema degli esploratori: statistica e scienza dei dati (retro-catalogo arXiv: annunci del 2026-09-30 in stat.ML).
Categorie arXiv: Methodology (stat.ME) ; Computation (stat.CO); Machine Learning (stat.ML).
Pagina del lavoro: https://arxiv.org/abs/2609.36142 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-07T17:33:44.747Z dalla pagina https://arxiv.org/catchup/stat.ML/2026-09-30?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).